Edit Profile Fraenkel, L. Edward Compute Distance To: Compute Author ID: fraenkel.l-edward Published as: Fraenkel, L.; Fraenkel, L. E.; Fraenkel, L. Edward External Links: MGP · Wikidata · GND Documents Indexed: 55 Publications since 1953, including 2 Books all top 5 Co-Authors 37 single-authored 7 Berger, Melvyn S. 5 Amick, Charles J. 1 Brézis, Haïm 1 Harwin, Petra J. 1 Keady, Grant 1 McLeod, John Bryce 1 Preston, Mark D. 1 Toland, John Francis 1 Watson, Richard E. all top 5 Serials 6 Journal of Fluid Mechanics 4 Archive for Rational Mechanics and Analysis 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Acta Mathematica 2 Quarterly Journal of Mechanics and Applied Mathematics 2 Journal of the London Mathematical Society. Second Series 2 European Journal of Applied Mathematics 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Proceedings of the Cambridge Philosophical Society 2 Cambridge Tracts in Mathematics 1 Communications in Mathematical Physics 1 Journal of Engineering Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Mathematika 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Journal of Non-Newtonian Fluid Mechanics 1 Bulletin of the American Mathematical Society. New Series 1 Computational Methods and Function Theory 1 Bulletin of the American Mathematical Society 1 Journal of Mathematics and Mechanics 1 Journal of the Aeronautical Sciences all top 5 Fields 21 Partial differential equations (35-XX) 20 Fluid mechanics (76-XX) 6 Functional analysis (46-XX) 3 Potential theory (31-XX) 3 Operator theory (47-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Integral equations (45-XX) 1 Number theory (11-XX) 1 Integral transforms, operational calculus (44-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 42 Publications have been cited 675 times in 545 Documents Cited by ▼ Year ▼ An introduction to maximum principles and symmetry in elliptic problems. Zbl 0947.35002Fraenkel, L. E. 120 2000 On the Stokes conjecture for the wave of extreme form. Zbl 0495.76021Amick, C. J.; Fraenkel, L. E.; Toland, J. F. 88 1982 A global theory of steady vortex rings in an ideal fluid. Zbl 0282.76014Fraenkel, L. E.; Berger, M. S. 78 1974 Examples of steady vortex rings of small cross-section in an ideal fluid. Zbl 0231.76013Fraenkel, L. E. 51 1972 Laminar flow in symmetrical channels with slightly curved walls. I. On the Jeffery-Hamel solutions for flow between plane walls. Zbl 0104.42403Fraenkel, L. E. 39 1962 Nonlinear desingularization in certain free-boundary problems. Zbl 0454.35087Berger, M. S.; Fraenkel, L. E. 38 1980 On steady vortex rings of small cross-section in an ideal fluid. Zbl 0195.55101Fraenkel, L. E. 37 1970 The uniqueness of Hill’s spherical vortex. Zbl 0609.76018Amick, C. J.; Fraenkel, L. E. 25 1986 Formulae for high derivatives of composite functions. Zbl 0388.46032Fraenkel, L. E. 25 1978 On the asymptotic solution of a nonlinear Dirichlet problem. Zbl 0203.10402Berger, M. S.; Fraenkel, L. E. 21 1970 On regularity of the boundary in the theory of Sobolev spaces. Zbl 0406.46026Fraenkel, L. E. 17 1979 A lower bound for electrostatic capacity in the plane. Zbl 0466.31007Fraenkel, L. E. 13 1981 On the behavior near the crest of waves of extreme form. Zbl 0617.76015Amick, C. J.; Fraenkel, L. E. 11 1987 A constructive existence proof for the extreme Stokes wave. Zbl 1105.76014Fraenkel, L. Edward 10 2007 The uniqueness of a family of steady vortex rings. Zbl 0694.76011Amick, C. J.; Fraenkel, L. E. 10 1988 Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types. Zbl 0439.76018Amick, C. J.; Fraenkel, L. E. 9 1980 On the method of matched asymptotic expansions. I: A matching principle. II: Some applications of the composite series. III: Two boundary-value problems. Zbl 0187.24104Fraenkel, L. E. 9 1969 On corner eddies in plane inviscid shear flow. Zbl 0113.40602Fraenkel, L. 8 1961 On singular perturbations of nonlinear operator equations. Zbl 0218.47031Berger, M. S.; Fraenkel, L. E. 7 1971 Laminar flow in symmetrical channels with slightly curved walls. II: An asymptotic series for the stream function. Zbl 0109.43701Fraenkel, L. E. 5 1963 A shallow-liquid theory in magnetohydrodynamics. Zbl 0087.20404Fraenkel, L. E. 5 1960 On steady vortex rings with swirl and a Sobolev inequality. Zbl 0821.46041Fraenkel, L. E. 4 1993 On the embedding of \(C_1(\Omega)\) in \(C^{0,\alpha}(\Omega)\). Zbl 0503.46017Fraenkel, L. E. 4 1982 A global theory of steady vortex rings in an ideal fluid. Zbl 0267.76012Fraenkel, L. E.; Berger, M. S. 4 1973 On a theory of laminar flow in channels of a certain class. Zbl 0265.76039Fraenkel, L. E. 4 1973 On the entry of a wedge into water: the thin wedge and an all-purpose boundary-layer equation. Zbl 1041.76503Fraenkel, L. E.; Keady, G. 3 2004 Some results for the entry of a blunt wedge into water. Zbl 0884.76005Fraenkel, L. E.; McLeod, J. B. 3 1997 The capacity of slender toroidal sets in \({\mathbb{R}{}}^ N\). Zbl 0755.31005Fraenkel, L. E. 3 1992 On nonlinear desingularization. Zbl 0432.35015Berger, M. S.; Fraenkel, L. E. 3 1980 A functional with prescribed initial derivatives in different Banach spaces. Zbl 0388.46026Brézis, Haïm; Fraenkel, L. E. 3 1978 On the flow of rotating fluid past bodies in a pipe. Zbl 0066.42401Fraenkel, L. E. 3 1955 An introduction to maximum principles and symmetry in elliptic problems. Reprint of the 2000 hardback edition. Zbl 1214.35001Fraenkel, L. E. 2 2011 On regularized distance and related functions. Zbl 0415.41026Fraenkel, L. E. 2 1979 On Benjamin’s theory of conjugate vortex flows. Zbl 0149.45103Fraenkel, L. E. 2 1967 A cylindrical sound pulse in a rotating gas. Zbl 0117.22102Fraenkel, L. E. 2 1959 The behaviour near the crest of an extreme Stokes wave. Zbl 1198.35177Fraenkel, L. E. 1 2010 On the local uniqueness and the profile of the extreme Stokes wave. Zbl 1198.35178Fraenkel, L. E.; Harwin, P. J. 1 2010 On the increase of capacity with asymmetry. Zbl 1156.31005Fraenkel, L. E. 1 2008 On a linear, partly hyperbolic model of viscoelastic flow past a plate. Zbl 0705.76004Fraenkel, L. E. 1 1990 Completeness properties in \(L_ 2\) of the eigenfunctions of two semi- linear differential operators. Zbl 0451.34023Fraenkel, L. E. 1 1980 Boundary-value problems for the steady Navier-Stokes equations. Zbl 0331.35051Fraenkel, L. E. 1 1976 The formulation of a uniform approximation for thin conical wings with sonic leading edges. Zbl 0117.19803Fraenkel, L. E.; Watson, R. 1 1964 An introduction to maximum principles and symmetry in elliptic problems. Reprint of the 2000 hardback edition. Zbl 1214.35001Fraenkel, L. E. 2 2011 The behaviour near the crest of an extreme Stokes wave. Zbl 1198.35177Fraenkel, L. E. 1 2010 On the local uniqueness and the profile of the extreme Stokes wave. Zbl 1198.35178Fraenkel, L. E.; Harwin, P. J. 1 2010 On the increase of capacity with asymmetry. Zbl 1156.31005Fraenkel, L. E. 1 2008 A constructive existence proof for the extreme Stokes wave. Zbl 1105.76014Fraenkel, L. Edward 10 2007 On the entry of a wedge into water: the thin wedge and an all-purpose boundary-layer equation. Zbl 1041.76503Fraenkel, L. E.; Keady, G. 3 2004 An introduction to maximum principles and symmetry in elliptic problems. Zbl 0947.35002Fraenkel, L. E. 120 2000 Some results for the entry of a blunt wedge into water. Zbl 0884.76005Fraenkel, L. E.; McLeod, J. B. 3 1997 On steady vortex rings with swirl and a Sobolev inequality. Zbl 0821.46041Fraenkel, L. E. 4 1993 The capacity of slender toroidal sets in \({\mathbb{R}{}}^ N\). Zbl 0755.31005Fraenkel, L. E. 3 1992 On a linear, partly hyperbolic model of viscoelastic flow past a plate. Zbl 0705.76004Fraenkel, L. E. 1 1990 The uniqueness of a family of steady vortex rings. Zbl 0694.76011Amick, C. J.; Fraenkel, L. E. 10 1988 On the behavior near the crest of waves of extreme form. Zbl 0617.76015Amick, C. J.; Fraenkel, L. E. 11 1987 The uniqueness of Hill’s spherical vortex. Zbl 0609.76018Amick, C. J.; Fraenkel, L. E. 25 1986 On the Stokes conjecture for the wave of extreme form. Zbl 0495.76021Amick, C. J.; Fraenkel, L. E.; Toland, J. F. 88 1982 On the embedding of \(C_1(\Omega)\) in \(C^{0,\alpha}(\Omega)\). Zbl 0503.46017Fraenkel, L. E. 4 1982 A lower bound for electrostatic capacity in the plane. Zbl 0466.31007Fraenkel, L. E. 13 1981 Nonlinear desingularization in certain free-boundary problems. Zbl 0454.35087Berger, M. S.; Fraenkel, L. E. 38 1980 Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types. Zbl 0439.76018Amick, C. J.; Fraenkel, L. E. 9 1980 On nonlinear desingularization. Zbl 0432.35015Berger, M. S.; Fraenkel, L. E. 3 1980 Completeness properties in \(L_ 2\) of the eigenfunctions of two semi- linear differential operators. Zbl 0451.34023Fraenkel, L. E. 1 1980 On regularity of the boundary in the theory of Sobolev spaces. Zbl 0406.46026Fraenkel, L. E. 17 1979 On regularized distance and related functions. Zbl 0415.41026Fraenkel, L. E. 2 1979 Formulae for high derivatives of composite functions. Zbl 0388.46032Fraenkel, L. E. 25 1978 A functional with prescribed initial derivatives in different Banach spaces. Zbl 0388.46026Brézis, Haïm; Fraenkel, L. E. 3 1978 Boundary-value problems for the steady Navier-Stokes equations. Zbl 0331.35051Fraenkel, L. E. 1 1976 A global theory of steady vortex rings in an ideal fluid. Zbl 0282.76014Fraenkel, L. E.; Berger, M. S. 78 1974 A global theory of steady vortex rings in an ideal fluid. Zbl 0267.76012Fraenkel, L. E.; Berger, M. S. 4 1973 On a theory of laminar flow in channels of a certain class. Zbl 0265.76039Fraenkel, L. E. 4 1973 Examples of steady vortex rings of small cross-section in an ideal fluid. Zbl 0231.76013Fraenkel, L. E. 51 1972 On singular perturbations of nonlinear operator equations. Zbl 0218.47031Berger, M. S.; Fraenkel, L. E. 7 1971 On steady vortex rings of small cross-section in an ideal fluid. Zbl 0195.55101Fraenkel, L. E. 37 1970 On the asymptotic solution of a nonlinear Dirichlet problem. Zbl 0203.10402Berger, M. S.; Fraenkel, L. E. 21 1970 On the method of matched asymptotic expansions. I: A matching principle. II: Some applications of the composite series. III: Two boundary-value problems. Zbl 0187.24104Fraenkel, L. E. 9 1969 On Benjamin’s theory of conjugate vortex flows. Zbl 0149.45103Fraenkel, L. E. 2 1967 The formulation of a uniform approximation for thin conical wings with sonic leading edges. Zbl 0117.19803Fraenkel, L. E.; Watson, R. 1 1964 Laminar flow in symmetrical channels with slightly curved walls. II: An asymptotic series for the stream function. Zbl 0109.43701Fraenkel, L. E. 5 1963 Laminar flow in symmetrical channels with slightly curved walls. I. On the Jeffery-Hamel solutions for flow between plane walls. Zbl 0104.42403Fraenkel, L. E. 39 1962 On corner eddies in plane inviscid shear flow. Zbl 0113.40602Fraenkel, L. 8 1961 A shallow-liquid theory in magnetohydrodynamics. Zbl 0087.20404Fraenkel, L. E. 5 1960 A cylindrical sound pulse in a rotating gas. Zbl 0117.22102Fraenkel, L. E. 2 1959 On the flow of rotating fluid past bodies in a pipe. Zbl 0066.42401Fraenkel, L. E. 3 1955 all cited Publications top 5 cited Publications all top 5 Cited by 666 Authors 17 Constantin, Adrian 17 Fraenkel, L. Edward 12 Ehrnström, Mats 10 Amick, Charles J. 9 Cao, Daomin 7 Escher, Joachim 6 Martin, Calin-Iulian 6 Matioc, Bogdan-Vasile 6 Vărvărucă, Eugen 6 Wang, Guodong 6 Weiss, Georg Sebastian 5 Kop’ev, V. F. 5 Magnanini, Rolando 5 Peng, Shuangjie 5 Strauss, Walter Alexander 5 Walsh, Samuel 4 Basu, Biswajit 4 Berestycki, Henri 4 Berger, Melvyn S. 4 Chen, Robin Ming 4 Chernyshev, S. A. 4 Friedman, Avner 4 Ganji, Davood Domiri 4 Huang, Xiaotao 4 Li, Congming 4 Lyons, Tony 4 Marchioro, Carlo 4 Maslov, Viktor Pavlovich 4 Mohyud-Din, Syed Tauseef 4 Poláčik, Peter 4 Shafarevich, Andreĭ Igorevich 4 Van Schaftingen, Jean 4 Vitolo, Antonio 4 Wheeler, Miles H. 4 Xiao, Jie 3 Ambrosetti, Antonio 3 Ball, John M. 3 Bensid, Sabri 3 Burton, Geoffrey R. 3 Ciraolo, Giulio 3 Eagles, P. M. 3 Elcrat, Alan R. 3 Fukumoto, Yasuhide 3 Henry, David 3 Hmidi, Taoufik 3 Hur, Vera Mikyoung 3 Ionescu-Kruse, Delia 3 Keady, Grant 3 Lei, Yutian 3 Leoni, Giovanni 3 Makinde, Oluwole Daniel 3 Mi, Yongsheng 3 Miller, Kenneth G. 3 Moffatt, Henry Keith 3 Mu, Chunlai 3 Mustafa, Octavian G. 3 Pileckas, Konstantin 3 Sakaguchi, Shigeru 3 Semenov, Yuriy A. 3 Sweers, Guido H. 3 Tadie 3 Toland, John Francis 3 Xin, Zhouping 3 Yan, Shusen 2 Ahmed, Naveed 2 Akinshin, R. V. 2 Akulenko, Leonid Denisovich 2 Aragona, Jorge 2 Ashton, Anthony C. L. 2 Bansal, Mohit 2 Bao, Jiguang 2 Berezovskij, A. A. 2 Biagioni, Hebe A. 2 Bianchi, Gabriele 2 Boucherif, Abdelkader 2 Bouguima, Sidi Mohamed 2 Brandolini, Barbara 2 Caffarelli, Luis Ángel 2 Caginalp, Gunduz 2 Clamond, Didier 2 Danaila, Ionut 2 Das, Debopam 2 De Silva, Daniela 2 Duffy, Brian Reginald 2 Durst, Franz 2 Emamizadeh, Behrouz 2 Encinas, L. Hernández 2 Esmaeilpour, M. 2 Gao, Lei 2 Gardner, Richard J. 2 Gronchi, Paolo 2 Guo, Boling 2 Henry, David 2 Hewett, David P. 2 Himonas, A. Alexandrou 2 Huberson, Serge G. 2 Jiang, Furu 2 Jiu, Quansen 2 Kalisch, Henrik 2 Kaplanskij, F. B. ...and 566 more Authors all top 5 Cited in 166 Serials 39 Journal of Fluid Mechanics 30 Archive for Rational Mechanics and Analysis 23 Journal of Differential Equations 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 Journal of Mathematical Analysis and Applications 12 Journal of Mathematical Fluid Mechanics 10 Fluid Dynamics 10 Physics of Fluids 9 Proceedings of the American Mathematical Society 9 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Journal of Functional Analysis 8 Transactions of the American Mathematical Society 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Nonlinear Analysis. Theory, Methods & Applications 7 Journal of Engineering Mathematics 7 Nonlinear Analysis. Real World Applications 6 Journal of Computational Physics 6 Rocky Mountain Journal of Mathematics 6 Advances in Mathematics 6 Applied Mathematics and Computation 6 Physica D 6 Communications in Partial Differential Equations 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Calculus of Variations and Partial Differential Equations 6 Journal of Nonlinear Mathematical Physics 5 Communications in Mathematical Physics 5 Journal d’Analyse Mathématique 5 Journal of Mathematical Physics 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Mathematische Annalen 5 European Journal of Mechanics. B. Fluids 5 Communications on Pure and Applied Analysis 4 Computers & Mathematics with Applications 4 Communications on Pure and Applied Mathematics 4 Mathematical Methods in the Applied Sciences 4 Wave Motion 4 Theoretical and Computational Fluid Dynamics 4 Acta Mathematica 4 Numerical Functional Analysis and Optimization 4 Studies in Applied Mathematics 4 Bulletin of the American Mathematical Society. New Series 4 Discrete and Continuous Dynamical Systems 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Acta Mechanica 3 Applicable Analysis 3 Computers and Fluids 3 Duke Mathematical Journal 3 Journal of Computational and Applied Mathematics 3 Mathematika 3 Monatshefte für Mathematik 3 Mathematical Problems in Engineering 3 Journal of Evolution Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Fluids 2 Journal of Applied Mathematics and Mechanics 2 Mathematical Notes 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 Inventiones Mathematicae 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Rendiconti del Seminario Matematico della Università di Padova 2 Applied Mathematics and Mechanics. (English Edition) 2 Revista Matemática Iberoamericana 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 European Journal of Applied Mathematics 2 Applied Mathematical Modelling 2 Potential Analysis 2 Journal of Mathematical Sciences (New York) 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Integral Transforms and Special Functions 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Bulletin of the American Mathematical Society 2 Complex Variables and Elliptic Equations 2 Discrete and Continuous Dynamical Systems. Series S 2 Analysis and Mathematical Physics 2 International Journal of Applied and Computational Mathematics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Analysis Mathematica 1 Archive for History of Exact Sciences 1 Bulletin of the Australian Mathematical Society 1 Communications in Algebra 1 Discrete Applied Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 1 Reviews of Modern Physics 1 Studia Mathematica 1 Theoretical and Mathematical Physics 1 Physics of Fluids, A 1 Mathematics of Computation 1 Journal of Geometry and Physics 1 Prikladnaya Matematika i Mekhanika 1 Applied Mathematics and Optimization 1 Archiv der Mathematik ...and 66 more Serials all top 5 Cited in 47 Fields 306 Partial differential equations (35-XX) 305 Fluid mechanics (76-XX) 34 Ordinary differential equations (34-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 24 Numerical analysis (65-XX) 22 Functional analysis (46-XX) 18 Potential theory (31-XX) 16 Integral equations (45-XX) 16 Geophysics (86-XX) 14 Operator theory (47-XX) 12 Mechanics of deformable solids (74-XX) 9 Real functions (26-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Global analysis, analysis on manifolds (58-XX) 8 Biology and other natural sciences (92-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Differential geometry (53-XX) 6 Probability theory and stochastic processes (60-XX) 5 Measure and integration (28-XX) 5 Approximations and expansions (41-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functions of a complex variable (30-XX) 4 Convex and discrete geometry (52-XX) 4 Mechanics of particles and systems (70-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 General topology (54-XX) 3 Optics, electromagnetic theory (78-XX) 3 Quantum theory (81-XX) 3 Operations research, mathematical programming (90-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Category theory; homological algebra (18-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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