Edit Profile (opens in new tab) Helffer, Bernard Compute Distance To: Compute Author ID: helffer.bernard Published as: Helffer, Bernard; Helffer, B. External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 312 Publications since 1972, including 9 Books 1 Further Contribution Reviewing Activity: 188 Reviews Co-Authors: 87 Co-Authors with 244 Joint Publications 1,715 Co-Co-Authors all top 5 Co-Authors 68 single-authored 29 Sjöstrand, Johannes 19 Hoffmann-Ostenhof, Thomas 16 Bolley, Catherine 16 Robert, Didier 15 Bérard, Pierre H. 14 Nourrigat, Jean Francois 12 Almog, Yaniv 11 Fournais, Søren 11 Kordyukov, Yuri A. 8 Kachmar, Ayman 8 Sundqvist, Mikael Persson 8 Siedentop, Heinz Karl Heinrich 7 Pan, Xingbin 6 Morame, Abderemane 5 Bolley, Pierre 5 Bonnaillie-Noël, Virginie 5 Camus, Jacques 5 Cornean, Horia D. 5 Grebenkov, Denis S. 5 Purice, Radu 4 Barbaroux, Jean-Marie 4 Nier, Francis 3 Derridj, Makhlouf 3 Gittins, Katie 3 Hoffmann-Ostenhof, Maria 3 Kiwan, Rola 3 Terracini, Susanna 3 Zuily, Claude 2 Bach, Volker 2 Belaud, Yves 2 Bodineau, Thierry 2 Dauge, Monique 2 Henry, Raphaël 2 Lafitte, Olivier D. 2 Martinez, André 2 Nadirashvili, Nikolai S. 2 Nourrigat, F. 2 Pankrashkin, Konstantin 2 Ramond, Thierry 2 Raymond, Nicolas 2 Rodino, Luigi 2 Véron, Laurent 2 Wang, Xue Ping 1 Aftalion, Amandine 1 Ancona, Alano 1 Averous, Genevieve 1 Balslev, Erik 1 Beauchard, Karine 1 Bérard Bergery, Lionel 1 Bourguignon, Jean-Pierre 1 Boutet de Monvel, Louis 1 Calabi, Eugenio 1 Chanillo, Sagun 1 Charron, Philippe 1 Connes, Alain 1 Corwin, Lawrence J. 1 Damlakhi, Moustafa K. 1 Deschamps, Annie 1 Dutour-Sikiric, Mathieu 1 El Houakmi, Z. 1 Ezin, Jean-Pierre 1 Farkas, Walter 1 Foucher, Françoise 1 Frank, Rupert L. 1 Gallot, Sylvestre 1 Grigis, Alain 1 Haslinger, Friedrich 1 Ignat, Radu 1 Jauberteau, François 1 Kannai, Yakar 1 Kerdelhué, Philippe 1 Kerdelhué, Phillippe 1 Klein, Markus 1 Knauf, Andreas 1 Kovařík, Hynek 1 Laleg-Kirati, Taous-Meriem 1 Laptev, Ari 1 Léna, Corentin 1 Liu, Qinghui 1 Mattera, Claude 1 Moutal, Nicolas 1 Owen, Mark P. 1 Owen, Markus Roger 1 Parisse, Bernard 1 Pham the Lai 1 Polombo, Albert 1 Qu, Yanhui 1 Robbiano, Luc 1 Rothschild, Linda Preiss 1 Royo-Letelier, Jimena 1 Vial, Grégory 1 Vũ Ngọc, San 1 Weikard, Rudi 1 Weissler, Fred B. 1 Yau, Shing-Tung 1 Zhou, Qi all top 5 Serials 13 Communications in Mathematical Physics 12 Journal of Functional Analysis 12 Communications in Partial Differential Equations 8 Asymptotic Analysis 8 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 7 Annales de l’Institut Fourier 7 Mémoires de la Société Mathématique de France. Nouvelle Série 7 Annales de l’Institut Henri Poincaré. Physique Théorique 6 Reviews in Mathematical Physics 5 Letters in Mathematical Physics 5 Transactions of the American Mathematical Society 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Archive for Rational Mechanics and Analysis 4 Gazette des Mathématiciens 4 Journal of Differential Equations 4 SIAM Journal on Mathematical Analysis 4 Séminaire Équations aux Dérivées Partielles 4 Moscow Mathematical Journal 4 Journal of Spectral Theory 3 Journal of Mathematical Physics 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 European Journal of Applied Mathematics 3 Documenta Mathematica 3 Bulletin de la Société Mathématique de France. Supplément. Mémoires 3 Annales Mathématiques du Québec 2 Helvetica Physica Acta 2 American Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Duke Mathematical Journal 2 Proceedings of the American Mathematical Society 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Calculus of Variations and Partial Differential Equations 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Nonlinear Studies 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Journal of the European Mathematical Society (JEMS) 2 Annales Henri Poincaré 2 Portugaliae Mathematica. Nova Série 2 Astérisque 2 Lecture Notes in Mathematics 2 Journal of Physics A: Mathematical and Theoretical 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Arkiv för Matematik 1 Bulletin of the London Mathematical Society 1 Colloquium Mathematicum 1 Indiana University Mathematics Journal 1 Integral Equations and Operator Theory 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Rendiconti del Seminario Matematico 1 Advances in Applied Mathematics 1 Physica D 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Cahiers Mathématiques 1 Algebra i Analiz 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Expositiones Mathematicae 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Advances in Mathematical Sciences and Applications 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Experimental Mathematics 1 Journal of the Egyptian Mathematical Society 1 Mathematical Physics Electronic Journal 1 Discrete and Continuous Dynamical Systems 1 Matemática Contemporânea 1 Functional Differential Equations 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Contemporary Mathematics 1 Milan Journal of Mathematics 1 Cubo 1 Bollettino della Unione Matematica Italiana. Series V. B 1 Bulletin of the American Mathematical Society 1 Cambridge Studies in Advanced Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Progress in Mathematics 1 SMF Journée Annuelle 1 Analysis & PDE 1 Confluentes Mathematici 1 Annals of the University of Bucharest. Mathematical Series 1 Progress in Nonlinear Differential Equations and Their Applications 1 Pure and Applied Analysis all top 5 Fields 263 Partial differential equations (35-XX) 86 Quantum theory (81-XX) 57 Statistical mechanics, structure of matter (82-XX) 55 Global analysis, analysis on manifolds (58-XX) 50 Operator theory (47-XX) 26 Ordinary differential equations (34-XX) 12 Numerical analysis (65-XX) 11 Topological groups, Lie groups (22-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Optics, electromagnetic theory (78-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 History and biography (01-XX) 4 Fluid mechanics (76-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Functional analysis (46-XX) 3 Mechanics of particles and systems (70-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Abstract harmonic analysis (43-XX) 2 Probability theory and stochastic processes (60-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 266 Publications have been cited 3,567 times in 1,825 Documents Cited by ▼ Year ▼ Multiple wells in the semi-classical limit. I. Zbl 0546.35053Helffer, B.; Sjöstrand, J. 222 1984 Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians. Zbl 1072.35006Helffer, Bernard; Nier, Francis 114 2005 Spectral methods in surface superconductivity. Zbl 1256.35001Fournais, Søren; Helffer, Bernard 109 2010 Semi-classical analysis for the Schrödinger operator and applications. Zbl 0647.35002Helffer, Bernard 106 1988 Equation de Schrödinger avec champ magnétique et équation de Harper. (The Schrödinger equation with magnetic field and the Harper equation). Zbl 0699.35189Helffer, B.; Sjöstrand, J. 94 1989 Calcul fonctionnel par la transformation de Mellin et opérateurs admissibles. Zbl 0524.35103Helffer, B.; Robert, D. 92 1983 Résonances en limite semi-classique. (Resonances in semi-classical limit). Zbl 0631.35075Helffer, B.; Sjöstrand, J. 85 1986 Magnetic bottles in connection with superconductivity. Zbl 1078.81023Helffer, Bernard; Morame, Abderemane 74 2001 Théorie spectrale pour des opérateurs globalement elliptiques. Zbl 0541.35002Helffer, Bernard 72 1984 Caractérisation des opérateurs hypoelliptiques homogenes invariants à gauche sur un groupe de Lie nilpotent gradue. Zbl 0423.35040Helffer, B.; Nourrigat, J. 72 1979 Nodal domains and spectral minimal partitions. Zbl 1171.35083Helffer, B.; Hoffmann-Ostenhof, T.; Terracini, S. 66 2009 Ergodicité et limite semi-classique. (Ergodicity and semi-classical limit). Zbl 0624.58039Helffer, B.; Martinez, A.; Robert, D. 62 1987 Puits multiples en mécanique semi-classique. IV: Étude du complexe de Witten. (Multiple wells in semi-classical limit. IV: Investigation of the Witten complex). Zbl 0597.35024Helffer, B.; Sjöstrand, J. 61 1985 Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique). (Semiclassical analysis for the Harper equation (with application to the magnetic Schrödinger equation)). Zbl 0714.34130Helffer, B.; Sjöstrand, J. 54 1988 Puits multiples en limite semi-classique. II: Interaction moléculaire. Symétries. Perturbation. (Multiple wells in the semi-classical limit. II: Molecular interaction. Symmetry. Perturbation). Zbl 0595.35031Helffer, B.; Sjöstrand, J. 53 1985 Eigenvalues variation. I: Neumann problem for Sturm–Liouville operators. Zbl 0784.34021Dauge, Monique; Helffer, Bernard 49 1993 Semi-classical analysis for Harper’s equation. III: Cantor structure of the spectrum. Zbl 0725.34099Helffer, B.; Sjöstrand, J. 48 1989 On the correlation for Kac-like models in the convex case. Zbl 0946.35508Helffer, Bernard; Sjöstrand, Johannes 46 1994 Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells. Zbl 0851.58046Helffer, Bernard; Mohamed, Arbderemane 45 1996 Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. (Maximal hypoellipticity for polynomial operators of vector fields). Zbl 0568.35003Helffer, Bernard; Nourrigat, Jean 43 1985 Nodal sets for ground states of Schrödinger operators with zero magnetic field in non simply connected domains. Zbl 1042.81012Helffer, B.; Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Owen, M. P. 42 1999 Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques. Zbl 0451.35022Robert, D.; Helffer, B. 41 1981 Spectral theory and its applications. Zbl 1279.47002Helffer, Bernard 41 2013 Propriétés asymptotiques du spectre d’opérateurs pseudodifferentiels sur \(R^ n\). Zbl 0501.35081Helffer, Bernard; Robert, Didier 40 1982 Caractérisation du spectre essentiel de l’opérateur de Schrödinger avec un champ magnétique. (Characterization of the essential spectrum of the Schrödinger operator with a magnetic field). Zbl 0638.47047Helffer, B.; Mohamed, A. 37 1988 Asymptotic of the density of states for the Schrödinger operator with periodic electric potential. Zbl 0951.35104Helffer, Bernard; Mohamed, Abderemane 34 1998 Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach. Zbl 1079.58025Helffer, Bernard; Klein, Markus; Nier, Francis 34 2004 Semiclassical analysis, Witten Laplacians, and statistical mechanics. Zbl 1046.82001Helffer, Bernard 33 2002 Multiple wells in the semi-classical limit. III: Interaction through non- resonant wells. Zbl 0597.35023Helffer, B.; Sjöstrand, J. 32 1985 Puits de potentiel généralisés et asymptotique semi-classique. (Generalized potential wells and semiclassical asymptotic). Zbl 0565.35082Helffer, B.; Robert, D. 32 1984 Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian. Zbl 1097.47020Fournais, Søren; Helffer, Bernard 30 2006 Analyse semi-classique pour l’équation de Harper. II: Comportement semi-classique près d’un rationnel. (Semiclassical analysis for the Harper equation. II. Semiclassical behaviour near a rational number). Zbl 0714.34131Helffer, B.; Sjöstrand, J. 30 1990 Paramètrixes d’opérateurs pseudodifferentiels à caractéristiques multiples. Zbl 0344.32009Boutet de Monvel, Louis; Grigis, Alain; Helffer, Bernard 28 1976 On diamagnetism and de Haas-van Alphen effect. Zbl 0715.35070Helffer, B.; Sjöstrand, J. 28 1990 Upper critical field and location of surface nucleation of superconductivity. (Champ surcritique et localisation de la nucléation de surface en supraconductivité.) Zbl 1060.35132Helffer, Bernard; Pan, Xing-Bin 27 2003 On the third critical field in Ginzburg-Landau theory. Zbl 1107.58009Fournais, S.; Helffer, B. 27 2006 On spectral minimal partitions: the case of the sphere. Zbl 1230.35072Helffer, Bernard; Hoffmann-Ostenhof, Thomas; Terracini, Susanna 26 2010 Limiting absorption principle and resonances for the Dirac operator. Zbl 0756.35062Balslev, E.; Helffer, B. 26 1992 Conditions necessaires d’hypoanalyticite pour des opérateurs invariants à gauche homogenes sur un groupe nilpotent gradue. Zbl 0458.35019Helffer, Bernard 26 1982 The log-Sobolev inequality for unbounded spin systems. Zbl 0972.82035Bodineau, T.; Helffer, B. 24 1999 Asymptotique des niveaux d’energie pour des Hamiltoniens à un degré de liberte. Zbl 0519.35063Helffer, B.; Robert, D. 23 1982 Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary. Zbl 1108.58018Nier, F.; Helffer, B. 23 2006 Effet tunnel pour l’équation de Schrödinger avec champ magnétique. (Tunnel effect for the Schrödinger equation with a magnetic field). Zbl 0699.35205Helffer, B.; Sjöstrand, J. 22 1987 On the stability of the relativistic electron-positron field. Zbl 1024.81056Bach, Volker; Barbaroux, Jean-Marie; Helffer, Bernard; Siedentop, Heinz 22 1999 On spectral minimal partitions: a survey. Zbl 1225.35158Helffer, B. 21 2010 Eigenvalues for the Robin Laplacian in domains with variable curvature. Zbl 1364.35215Helffer, Bernard; Kachmar, Ayman 20 2017 Degenerate parabolic operators of Kolmogorov type with a geometric control condition. Zbl 1311.93042Beauchard, Karine; Helffer, Bernard; Henry, Raphael; Robbiano, Luc 20 2015 Effet d’Aharonov-Bohm sur un état borné de l’équation de Schrödinger. (Aharonov-Bohm effect for a bounded state of the Schrödinger equation). Zbl 0702.35186Helffer, B. 19 1988 Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (general case). Zbl 1057.35061Helffer, Bernard; Morame, Abderemane 19 2004 Compactness of the solution operator to \(\overline\partial\) in weighted \(L^{2}\)-spaces. Zbl 1144.32023Haslinger, Friedrich; Helffer, Bernard 19 2007 Hypoellipticite pour des groupes nilpotents de rang de nilpotence 3. Zbl 0385.35015Helffer, B.; Nourrigat, F. 18 1978 Invariants associés à une classe d’opérateurs pseudodifférentiels et applications à l’hypoellipticité. Zbl 0301.35026Helffer, Bernard 17 1976 Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions. Zbl 1196.35031Bonnaillie-Noël, V.; Helffer, B.; Hoffmann-Ostenhof, T. 17 2009 An application of semi-classical analysis to the asymptotic study of the supercooling field of a superconducting material. Zbl 0779.35104Bolley, C.; Helffer, B. 17 1993 Magnetic bottles for the Neumann problem: the case of dimension 3. Zbl 1199.81016Helffer, Bernard; Morame, Abderemane 16 2002 The distribution of surface superconductivity along the boundary: on a conjecture of X. B. Pan. Zbl 1136.82042Almog, Yaniv; Helffer, Bernard 15 2007 Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: analysis near the bottom. Zbl 1184.35233Helffer, B.; Kordyukov, Y. A. 14 2009 Sur le spectre de l’équation de Dirac (dans \({\mathbb{R}}^ 2\) ou \({\mathbb{R}}^ 3)\) avec champ magnétique. (On the spectrum of the Dirac equation (in \({\mathbb{R}}^ 2\) or \({\mathbb{R}}^ 3)\) with magnetic field). Zbl 0703.35127Helffer, B.; Nourrigat, J.; Wang, X. P. 14 1989 On mathematical models for Bose-Einstein condensates in optical lattices. Zbl 1171.82304Aftalion, Amandine; Helffer, Bernard 14 2009 Remarks on decay of correlations and Witten Laplacians Brascamp-Lieb inequalities and semiclassical limit. Zbl 0921.35141Helffer, Bernard 14 1998 Tunneling between corners for Robin Laplacians. Zbl 1319.35129Helffer, Bernard; Pankrashkin, Konstantin 14 2015 Numerical analysis of nodal sets for eigenvalues of Aharonov-Bohm Hamiltonians on the square with application to minimal partitions. Zbl 1270.35025Bonnaillie-Noël, V.; Helffer, B. 14 2011 Numerical simulations for nodal domains and spectral minimal partitions. Zbl 1191.35189Bonnaillie-Noël, Virginie; Helffer, Bernard; Vial, Gregory 13 2010 Remarks on decay of correlations and Witten Laplacians. III: Application to logarithmic Sobolev inequalities. Zbl 1055.82004Helffer, Bernard 13 1999 Strong diamagnetism for general domains and application. Zbl 1133.35073Fournais, Soeren; Helffer, Bernard 13 2007 Correlations, spectral gap and log-Sobolev inequalities for unbounded spins systems. Zbl 1161.82306Bodineau, T.; Helffer, B. 12 2000 Rigorous results for the Ginzburg-Landau equations associated to a superconducting film in the weak \(\kappa\) limit. Zbl 0864.35097Bolley, Catherine; Helffer, Bernard 12 1996 Tunneling for the Robin Laplacian in smooth planar domains. Zbl 1361.35119Helffer, Bernard; Kachmar, Ayman; Raymond, Nicolas 12 2017 On a magnetic characterization of spectral minimal partitions. Zbl 1282.35259Helffer, Bernard; Hoffmann-Ostenhof, Thomas 12 2013 Nonlinear eigenvalues and analytic hypoellipticity. Zbl 1053.35045Chanillo, Sagun; Helffer, Bernard; Laptev, Ari 12 2004 On the spectrum of non-selfadjoint Schrödinger operators with compact resolvent. Zbl 1332.35241Almog, Yaniv; Helffer, Bernard 12 2015 The complex Airy operator on the line with a semipermeable barrier. Zbl 1430.47001Grebenkov, Denis S.; Helffer, Bernard; Henry, Raphael 12 2017 On nodal domains in Euclidean balls. Zbl 1362.35200Helffer, Bernard; Sundqvist, Mikael Persson 11 2016 Sur l’hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 derivées). Zbl 0374.35012Helffer, Bernard 11 1977 Étude du spectre pour un opérateur globalement elliptique dont le symbole de Weyl présente des symétries. II: Action des groupes de Lie compacts. (Spectral study for a globally elliptic operator the Weyl symbol of which presents symmetries. II: Actions of compact Lie groups). Zbl 0605.58042Helffer, B.; Robert, D. 11 1986 On spectral theory for Schrödinger operators with magnetic potentials. Zbl 0816.35100Helffer, Bernard 11 1994 Splitting in large dimension and infrared estimates. II: Moment inequalities. Zbl 0920.35124Helffer, B. 11 1998 On a family of solutions to the second Painlevé equation related to superconductivity. Zbl 0920.34051Helffer, Bernard; Weissler, Fred B. 11 1998 On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current. Zbl 1223.82070Helffer, B. 11 2011 Nodal and spectral minimal partitions – The state of the art in 2016. Zbl 1373.49050Bonnaillie-Noël, Virginie; Helffer, Bernard 11 2017 The Ginzburg-Landau functional with vanishing magnetic field. Zbl 1331.35330Helffer, Bernard; Kachmar, Ayman 11 2015 Dirichlet eigenfunctions of the square membrane: Courant’s property, and A. Stern’s and Å. Pleijel’s analyses. Zbl 1390.35209Bérard, Pierre; Helffer, Bernard 11 2015 Energy asymptotics for type II superconductors. Zbl 1160.82365Fournais, S.; Helffer, B. 11 2005 Riesz means of bound states and semiclassical limit connected with a Lieb-Thirring’s conjecture. Zbl 0717.35062Helffer, B.; Robert, D. 11 1990 Long-time vanishing properties of solutions of some semilinear parabolic equations. Zbl 0983.35066Belaud, Yves; Helffer, Bernard; Véron, Laurent 10 2001 Eigenvalues variation. II: Multidimensional problems. Zbl 0807.34033Dauge, Monique; Helffer, Bernard 10 1993 Superconductivity between \(H_{C_2}\) and \(H_{C_3}\). Zbl 1225.34097Fournais, Søren; Helffer, Bernard; Persson, Mikael 10 2011 The Montgomery model revisited. Zbl 1207.34110Helffer, B. 10 2010 Nodal domains in the square – the Neumann case. Zbl 1342.35198Helffer, Bernard; Sundqvist, Mikael Persson 10 2015 On the Ginzburg-Landau critical field in three dimensions. Zbl 1159.35301Fournais, S.; Helffer, B. 10 2009 A review on large \(k\) minimal spectral \(k\)-partitions and Pleijel’s theorem. Zbl 1346.35132Helffer, B.; Hoffmann-Ostenhof, T. 9 2015 Sur une classe d’opérateurs partiellement hypoelliptiques. Zbl 0294.35021Bolley, P.; Camus, J.; Helffer, B. 9 1976 Puits multiples en mécanique semi-classique. V: Étude des minipuits. (Multiple wells in semi-classical mechanics. V: Study of miniwells). Zbl 0628.35024Helffer, B.; Sjöstrand, J. 9 1986 Analyticite et iterés reduits d’un système de champs de vecteurs. Zbl 0452.35123Helffer, B.; Mattera, Cl. 9 1980 On spectral properties of the Bloch-Torrey operator in two dimensions. Zbl 1387.35427Grebenkov, Denis S.; Helffer, Bernard 9 2018 On the Hartree-Fock equations of the electron-positron field. Zbl 1087.81055Barbaroux, Jean-Marie; Farkas, Walter; Helffer, Bernard; Siedentop, Heinz 9 2005 Converse spectral problems for nodal domains. Zbl 1125.35068Helffer, B.; Hoffmann-Ostenhof, T. 8 2007 Proof of the De Gennes formula for the superheating field in the weak \(\kappa\) limit. Zbl 0889.34010Bolley, Catherine; Helffer, Bernard 8 1997 The Ginzburg-Landau equations in a semi-infinite superconducting film in the large \(\kappa\) limit. Zbl 0891.35144Bolley, Catherine; Helffer, Bernard 8 1997 Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs. Zbl 0549.35026Helffer, B.; Nourrigat, J. 8 1983 Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip. Zbl 1477.58005Bérard, Pierre; Helffer, Bernard; Kiwan, Rola 2 2021 Improving semigroup bounds with resolvent estimates. Zbl 07367384Helffer, B.; Sjöstrand, J. 1 2021 On Courant’s nodal domain property for linear combinations of eigenfunctions. II. Zbl 1472.35250Bérard, Pierre; Helffer, Bernard 1 2021 Thin domain limit and counterexamples to strong diamagnetism. Zbl 1473.35523Helffer, Bernard; Kachmar, Ayman 1 2021 Sturm’s theorem on zeros of linear combinations of eigenfunctions. Zbl 1443.34026Bérard, Pierre; Helffer, Bernard 8 2020 Courant-sharp Robin eigenvalues for the square: the case with small Robin parameter. Zbl 1434.35025Gittins, K.; Helffer, B. 3 2020 Sturm’s theorem on the zeros of sums of eigenfunctions: Gelfand’s strategy implemented. Zbl 1472.34004Bérard, Pierre; Helffer, Bernard 2 2020 Inequalities for the lowest magnetic Neumann eigenvalue. Zbl 1415.35213Fournais, S.; Helffer, B. 4 2019 Courant-sharp Robin eigenvalues for the square and other planar domains. Zbl 1444.35118Gittins, Katie; Helffer, Bernard 4 2019 On a Schrödinger operator with a purely imaginary potential in the semiclassical limit. Zbl 1426.35099Almog, Y.; Grebenkov, D. S.; Helffer, B. 3 2019 On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator. III: Magnetic fields that change sign. Zbl 1415.35214Helffer, Bernard; Kovařík, Hynek; Sundqvist, Mikael P. 1 2019 Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator. Zbl 07057307Helffer, Bernard; Liu, Qinghui; Qu, Yanhui; Zhou, Qi 1 2019 Peierls’ substitution for low lying spectral energy windows. Zbl 1440.35053Cornean, Horia D.; Helffer, Bernard; Purice, Radu 1 2019 On spectral properties of the Bloch-Torrey operator in two dimensions. Zbl 1387.35427Grebenkov, Denis S.; Helffer, Bernard 9 2018 The density of superconductivity in domains with corners. Zbl 1454.35362Helffer, Bernard; Kachmar, Ayman 7 2018 Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains. Zbl 1386.81075Almog, Y.; Grebenkov, D. S.; Helffer, B. 5 2018 On Courant’s nodal domain property for linear combinations of eigenfunctions. I. Zbl 1403.35192Bérard, Pierre H.; Helffer, Bernard 4 2018 Pleijel’s theorem for Schrödinger operators with radial potentials. Zbl 1384.35048Charron, Philippe; Helffer, Bernard; Hoffmann-Ostenhof, Thomas 2 2018 A beals criterion for magnetic pseudo-differential operators proved with magnetic Gabor frames. Zbl 1407.35237Cornean, Horia D.; Helffer, Bernard; Purice, Radu 2 2018 Eigenvalues for the Robin Laplacian in domains with variable curvature. Zbl 1364.35215Helffer, Bernard; Kachmar, Ayman 20 2017 Tunneling for the Robin Laplacian in smooth planar domains. Zbl 1361.35119Helffer, Bernard; Kachmar, Ayman; Raymond, Nicolas 12 2017 The complex Airy operator on the line with a semipermeable barrier. Zbl 1430.47001Grebenkov, Denis S.; Helffer, Bernard; Henry, Raphael 12 2017 Nodal and spectral minimal partitions – The state of the art in 2016. Zbl 1373.49050Bonnaillie-Noël, Virginie; Helffer, Bernard 11 2017 On the semi-classical analysis of the ground state energy of the Dirichlet Pauli operator. Zbl 1356.81132Helffer, Bernard; Sundqvist, Mikael Persson 7 2017 Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality. Zbl 1386.35297Helffer, Bernard; Kiwan, Rola 5 2017 Decay of superconductivity away from the magnetic zero set. Zbl 1382.35285Helffer, Bernard; Kachmar, Ayman 4 2017 Low lying spectral gaps induced by slowly varying magnetic fields. Zbl 1372.35255Cornean, Horia D.; Helffer, Bernard; Purice, Radu 4 2017 On the semiclassical analysis of the ground state energy of the Dirichlet Pauli operator in non-simply connected domains. Zbl 1414.35134Helffer, Bernard; Persson Sundqvist, M. 3 2017 Mixed normal-superconducting states in the presence of strong electric currents. Zbl 1361.35171Almog, Yaniv; Helffer, Bernard; Pan, Xing-Bin 3 2017 From constant to non-degenerately vanishing magnetic fields in superconductivity. Zbl 1361.82039Helffer, Bernard; Kachmar, Ayman 2 2017 Some nodal properties of the quantum harmonic oscillator and other Schrödinger operators in \(\mathbb{R}^2\). Zbl 1391.35020Bérard, Pierre; Helffer, Bernard 1 2017 On nodal domains in Euclidean balls. Zbl 1362.35200Helffer, Bernard; Sundqvist, Mikael Persson 11 2016 Magnetic wells in dimension three. Zbl 1351.81053Helffer, Bernard; Kordyukov, Yuri; Raymond, Nicolas; Ngọc, San Vũ 8 2016 Chambers’s formula for the graphene and the Hou model with kagome periodicity and applications. Zbl 1341.82125Helffer, Bernard; Kerdelhué, Philippe; Royo-Letelier, Jimena 7 2016 Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle. Zbl 1382.58021Bérard, Pierre; Helffer, Bernard 7 2016 A. Stern’s analysis of the nodal sets of some families of spherical harmonics revisited. Zbl 1351.33014Bérard, P.; Helffer, B. 2 2016 The weak Pleijel theorem with geometric control. Zbl 1372.35194Bérard, Pierre; Helffer, Bernard 2 2016 Degenerate parabolic operators of Kolmogorov type with a geometric control condition. Zbl 1311.93042Beauchard, Karine; Helffer, Bernard; Henry, Raphael; Robbiano, Luc 20 2015 Tunneling between corners for Robin Laplacians. Zbl 1319.35129Helffer, Bernard; Pankrashkin, Konstantin 14 2015 On the spectrum of non-selfadjoint Schrödinger operators with compact resolvent. Zbl 1332.35241Almog, Yaniv; Helffer, Bernard 12 2015 The Ginzburg-Landau functional with vanishing magnetic field. Zbl 1331.35330Helffer, Bernard; Kachmar, Ayman 11 2015 Dirichlet eigenfunctions of the square membrane: Courant’s property, and A. Stern’s and Å. Pleijel’s analyses. Zbl 1390.35209Bérard, Pierre; Helffer, Bernard 11 2015 Nodal domains in the square – the Neumann case. Zbl 1342.35198Helffer, Bernard; Sundqvist, Mikael Persson 10 2015 A review on large \(k\) minimal spectral \(k\)-partitions and Pleijel’s theorem. Zbl 1346.35132Helffer, B.; Hoffmann-Ostenhof, T. 9 2015 Accurate semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator. Zbl 1338.81187Helffer, Bernard; Kordyukov, Yuri A. 6 2015 Nodal sets of eigenfunctions, Antonie Stern’s results revisited. Zbl 1379.35203Bérard, Pierre; Helffer, Bernard 4 2015 Edited extracts from Antonie Stern’s thesis. Zbl 1379.35204Bérard, Pierre; Helffer, Bernard 2 2015 Global stability of the normal state of superconductors in the presence of a strong electric current. Zbl 1304.35662Almog, Yaniv; Helffer, Bernard 8 2014 Minimal partitions for anisotropic tori. Zbl 1321.58006Helffer, Bernard; Hoffmann-Ostenhof, Thomas 4 2014 Semiclassical spectral asymptotics for a magnetic Schrödinger operator with non-vanishing magnetic field. Zbl 1317.81101Helffer, Bernard; Kordyukov, Yuri A. 4 2014 Remarks on the boundary set of spectral equipartitions. Zbl 1322.35006Bérard, P.; Helffer, B. 1 2014 Spectral theory and its applications. Zbl 1279.47002Helffer, Bernard 41 2013 On a magnetic characterization of spectral minimal partitions. Zbl 1282.35259Helffer, Bernard; Hoffmann-Ostenhof, Thomas 12 2013 Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field. Zbl 1267.82139Almog, Yaniv; Helffer, Bernard; Pan, Xing-Bin 8 2013 Sharp trace asymptotics for a class of \(2D\)-magnetic operators. (Asymptotiques précisées pour la trace d’une classe d’opérateurs de Schrödinger magnétiques en dimension 2.) Zbl 1301.35070Cornean, Horia D.; Fournais, Søren; Frank, Rupert L.; Helffer, Bernard 5 2013 On spectral minimal partitions: the disk revisited. Zbl 1389.35022Bonnaillie-Noël, Virginie; Helffer, Bernard 2 2013 Eigenvalue estimates for a three-dimensional magnetic Schrödinger operator. Zbl 1325.35123Helffer, Bernard; Kordyukov, Yuri A. 2 2013 Spectral minimal partitions for a thin strip on a cylinder or a thin annulus like domain with Neumann condition. Zbl 1273.35029Helffer, Bernard; Hoffmann-Ostenhof, Thomas 2 2013 Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field. II: The large conductivity limit. Zbl 1263.82074Almog, Yaniv; Helffer, Bernard; Pan, Xing-Bin 6 2012 Semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator II: The case of degenerate wells. Zbl 1247.35084Helffer, Bernard; Kordyukov, Yuri A. 5 2012 Numerical analysis of nodal sets for eigenvalues of Aharonov-Bohm Hamiltonians on the square with application to minimal partitions. Zbl 1270.35025Bonnaillie-Noël, V.; Helffer, B. 14 2011 On pseudo-spectral problems related to a time-dependent model in superconductivity with electric current. Zbl 1223.82070Helffer, B. 11 2011 Superconductivity between \(H_{C_2}\) and \(H_{C_3}\). Zbl 1225.34097Fournais, Søren; Helffer, Bernard; Persson, Mikael 10 2011 Introduction to some conjectures for spectral minimal partitions. Zbl 1247.35181Helffer, B. 7 2011 Semiclassical spectral asymptotics for a two-dimensional magnetic Schrödinger operator: the case of discrete wells. Zbl 1218.58017Helffer, Bernard; Kordyukov, Yuri A. 6 2011 Subellipticity and maximal hypoellipticity for two complex vector fields in \((2+2)\)-variables. Zbl 1235.35073Derridj, Makhlouf; Helffer, Bernard 2 2011 Spectral methods in surface superconductivity. Zbl 1256.35001Fournais, Søren; Helffer, Bernard 109 2010 On spectral minimal partitions: the case of the sphere. Zbl 1230.35072Helffer, Bernard; Hoffmann-Ostenhof, Thomas; Terracini, Susanna 26 2010 On spectral minimal partitions: a survey. Zbl 1225.35158Helffer, B. 21 2010 Numerical simulations for nodal domains and spectral minimal partitions. Zbl 1191.35189Bonnaillie-Noël, Virginie; Helffer, Bernard; Vial, Gregory 13 2010 The Montgomery model revisited. Zbl 1207.34110Helffer, B. 10 2010 Spectral properties of higher order anharmonic oscillators. Zbl 1302.47069Helffer, B.; Persson, M. 8 2010 Superconductivity near the normal state under the action of electric currents and induced magnetic fields in \(\mathbb R^2\). Zbl 1201.35179Almog, Yaniv; Helffer, Bernard; Pan, Xing-Bin 8 2010 On minimal partitions: new properties and applications to the disk. Zbl 1231.35011Helffer, Bernard; Hoffmann-Ostenhof, Thomas 7 2010 Nodal minimal partitions in dimension 3. Zbl 1193.35162Helffer, Bernard; Hoffmann-Ostenhof, Thomas; Terracini, Susanna 7 2010 Remarks on two notions of spectral minimal partitions. Zbl 1222.35067Helffer, Bernard; Hoffmann-Ostenhof, Thomas 6 2010 Bulk superconductivity in type II superconductors near the second critical field. Zbl 1188.82152Fournais, Soren; Helffer, Bernard 2 2010 Magnetic calculus and semiclassical trace formulas. Zbl 1204.81066Helffer, B.; Purice, R. 2 2010 On the subellipticity of some hypoelliptic quasihomogeneous systems of complex vector fields. Zbl 1201.35093Derridj, M.; Helffer, B. 1 2010 Nodal domains and spectral minimal partitions. Zbl 1171.35083Helffer, B.; Hoffmann-Ostenhof, T.; Terracini, S. 66 2009 Aharonov-Bohm Hamiltonians, isospectrality and minimal partitions. Zbl 1196.35031Bonnaillie-Noël, V.; Helffer, B.; Hoffmann-Ostenhof, T. 17 2009 Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: analysis near the bottom. Zbl 1184.35233Helffer, B.; Kordyukov, Y. A. 14 2009 On mathematical models for Bose-Einstein condensates in optical lattices. Zbl 1171.82304Aftalion, Amandine; Helffer, Bernard 14 2009 On the Ginzburg-Landau critical field in three dimensions. Zbl 1159.35301Fournais, S.; Helffer, B. 10 2009 Semiclassical analysis of Schrödinger operators with magnetic wells. Zbl 1184.81058Helffer, Bernard; Kordyukov, Yuri A. 2 2009 Subelliptic estimates for some systems of complex vector fields: Quasihomogeneous case. Zbl 1172.35367Derridj, M.; Helffer, B. 1 2009 Semiclassical asymptotics and gaps in the spectra of periodic Schrödinger operators with magnetic wells. Zbl 1131.35054Helffer, Bernard; Kordyukov, Yuri A. 4 2008 Reduced Landau-de Gennes functional and surface smectic state of liquid crystals. Zbl 1153.49003Helffer, Bernard; Pan, Xing-Bin 4 2008 Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells. Zbl 1156.81384Helffer, Bernard; Kordyukov, Yuri A. 2 2008 Periodic magnetic Schrödinger operators: spectral gaps and tunneling effect. Zbl 1237.58029Kordyukov, Yu. A.; Helffer, B. 1 2008 Compactness of the solution operator to \(\overline\partial\) in weighted \(L^{2}\)-spaces. Zbl 1144.32023Haslinger, Friedrich; Helffer, Bernard 19 2007 The distribution of surface superconductivity along the boundary: on a conjecture of X. B. Pan. Zbl 1136.82042Almog, Yaniv; Helffer, Bernard 15 2007 Strong diamagnetism for general domains and application. Zbl 1133.35073Fournais, Soeren; Helffer, Bernard 13 2007 Converse spectral problems for nodal domains. Zbl 1125.35068Helffer, B.; Hoffmann-Ostenhof, T. 8 2007 Optimal uniform elliptic estimates for the Ginzburg-Landau system. Zbl 1161.35042Fournais, S.; Helffer, B. 7 2007 The semiclassical regime for ablation front models. Zbl 1107.76081Helffer, Bernard; Lafitte, Olivier 3 2007 Nodal domains and spectral minimal partitions. (Domaines nodaux et partitions spectrales minimales.) Zbl 1216.35020Helffer, Bernard 1 2007 Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian. Zbl 1097.47020Fournais, Søren; Helffer, Bernard 30 2006 On the third critical field in Ginzburg-Landau theory. Zbl 1107.58009Fournais, S.; Helffer, B. 27 2006 Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary. Zbl 1108.58018Nier, F.; Helffer, B. 23 2006 ...and 166 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,473 Authors 134 Helffer, Bernard 39 Sjöstrand, Johannes 31 Kachmar, Ayman 30 Martinez, André 28 Raymond, Nicolas 28 Robert, Didier 20 Fournais, Søren 20 Pan, Xingbin 19 Ruzhansky, Michael V. 17 Almog, Yaniv 17 Gérard, Christian 17 Nourrigat, Jean Francois 17 Wang, Xueping 16 Bonnaillie-Noël, Virginie 16 Lewin, Mathieu 15 Cornean, Horia D. 15 Sundqvist, Mikael Persson 14 Hérau, Frédéric 14 Klein, Markus 14 Mughetti, Marco 13 Morame, Abderemane 13 Nicola, Fabio 13 Zworski, Maciej 12 Bérard, Pierre H. 12 Nakamura, Shu 12 Nier, Francis 12 Pankrashkin, Konstantin 12 Popoff, Nicolas 11 Klopp, Frédéric 11 Kordyukov, Yuri A. 11 Parmeggiani, Alberto 11 Purice, Radu 11 Rodino, Luigi 10 Abatangelo, Laura 10 Correggi, Michele 10 Derridj, Makhlouf 10 Léna, Corentin 10 Măntoiu, Marius Laurențiu 10 Rougerie, Nicolas 10 Sobolev, Alexander V. 9 Briet, Philippe 9 Bruneau, Vincent 9 Christ, Michael 9 Dimassi, Mouez 9 Felli, Veronica 9 Fujiié, Setsuro 9 Hainzl, Christian 9 Himonas, A. 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Yu. 8 Bolley, Catherine 8 Dobrokhotov, Sergei Yurievich 8 Fischer, Véronique 8 Frank, Rupert L. 8 Haslinger, Friedrich 8 Jitomirskaya, Svetlana Yakovlevna 8 Lelièvre, Tony 8 Levy-Bruhl, Pierre 8 Petronilho, Gerson 8 Ramond, Thierry 8 Rosenberger, Elke 8 Sigal, Israel Michael 8 Vũ Ngọc, San 7 Bony, Jean-François 7 Bove, Antonio 7 Dauge, Monique 7 Grigis, Alain 7 Hislop, Peter D. 7 Hoffmann-Ostenhof, Thomas 7 Kennedy, James Bernard 7 Le Peutrec, Dorian 7 Müller, Detlef 7 Ricci, Fulvio 7 Rothschild, Linda Preiss 7 Tamura, Hideo 7 Terracini, Susanna 7 Tokmagambetov, Niyaz Esenzholovich 7 Uribe, Alejandro 7 Wang, Xue Ping 6 Bambusi, Dario 6 Beauchard, Karine 6 Bismut, Jean-Michel 6 Cappiello, Marco 6 Chen, Hua 6 Exner, Pavel 6 Grebenkov, Denis S. 6 Hitrik, Michael 6 Iantchenko, Alexei 6 Iftimie, Viorel 6 Johnsen, Jon 6 Krejčiřík, David 6 Levendorskiĭ, Sergeĭ Zakharovich 6 Li, Weixi 6 Miyamoto, Yasuhito 6 Nectoux, Boris 6 Parnovski, Leonid 6 Raikov, Georgi D. ...and 1,373 more Authors all top 5 Cited in 267 Serials 146 Communications in Mathematical Physics 141 Journal of Functional Analysis 86 Journal of Mathematical Physics 74 Communications in Partial Differential Equations 55 Annales de l’Institut Henri Poincaré. 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