# zbMATH — the first resource for mathematics

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 Documents Indexed: 44 Publications since 1994
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#### Co-Authors

 2 single-authored 18 Dal Maso, Gianni 11 Fonda, Alessandro 4 Lazzaroni, Giuliano 3 Cortesani, Guido 3 Orlando, Gianluca 2 Almi, Stefano 2 Francfort, Gilles A. 2 Larsen, Christopher J. 1 Barroso, Ana Cristina 1 Cagnetti, Filippo 1 Ebobisse, François Bille 1 Fonseca, Irene 1 Negri, Matteo 1 Racca, Simone 1 Rossi, Riccarda 1 Thomas, Marita 1 Torres, Pedro José 1 Zanini, Chiara 1 Zanolin, Fabio
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#### Serials

 3 Archive for Rational Mechanics and Analysis 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Calculus of Variations and Partial Differential Equations 2 Discrete and Continuous Dynamical Systems 2 Advanced Nonlinear Studies 2 Bollettino dell’Unione Matematica Italiana. Series IX 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Numerical Functional Analysis and Optimization 1 Proceedings of the American Mathematical Society 1 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Rendiconti del Seminario Matematico della Università di Padova 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Asymptotic Analysis 1 Differential and Integral Equations 1 SIAM Journal on Applied Mathematics 1 Celestial Mechanics and Dynamical Astronomy 1 Journal of Dynamics and Differential Equations 1 Topological Methods in Nonlinear Analysis 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Interfaces and Free Boundaries 1 Discrete and Continuous Dynamical Systems. Series S 1 Advances in Calculus of Variations 1 Advances in Nonlinear Analysis 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

#### Fields

 21 Mechanics of deformable solids (74-XX) 19 Partial differential equations (35-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 10 Ordinary differential equations (34-XX) 5 Operator theory (47-XX) 3 Mechanics of particles and systems (70-XX) 2 Real functions (26-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 1 Measure and integration (28-XX) 1 Numerical analysis (65-XX) 1 Classical thermodynamics, heat transfer (80-XX)

#### Citations contained in zbMATH Open

39 Publications have been cited 634 times in 388 Documents Cited by Year
Quasistatic crack growth in nonlinear elasticity. Zbl 1064.74150
Dal Maso, Gianni; Francfort, Gilles A.; Toader, Rodica
2005
A model for the quasi-static growth of brittle fractures: Existence and approximation results. Zbl 1042.74002
2002
A density result in SBV with respect to non-isotropic energies. Zbl 0939.49024
1999
Periodic orbits of radially symmetric Keplerian-like systems: a topological degree approach. Zbl 1168.34031
2008
A model for crack propagation based on viscous approximation. Zbl 1277.74066
2011
A model for the quasi-static growth of brittle fractures based on local minimization. Zbl 1205.74149
2002
An artificial viscosity approach to quasistatic crack growth. Zbl 1180.35521
2009
Periodic solutions of radially symmetric perturbations of Newtonian systems. Zbl 1248.34051
2012
Radially symmetric systems with a singularity and asymptotically linear growth. Zbl 1218.34047
2011
A relaxation theorem in the space of functions of bounded deformation. Zbl 0960.49014
Barroso, Ana Cristina; Fonseca, Irene; Toader, Rodica
2000
Periodic solutions of singular radially symmetric systems with superlinear growth. Zbl 1251.34056
Fonda, Alessandro; Toader, Rodica; Zanolin, Fabio
2012
Periodic orbits of radially symmetric systems with a singularity: the repulsive case. Zbl 1241.34048
2011
Energy release rate and stress intensity factor in antiplane elasticity. Zbl 1228.35243
2011
Rate-independent damage in thermo-viscoelastic materials with inertia. Zbl 1412.35325
Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica
2018
2011
Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case. Zbl 1358.49015
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2016
Periodic solutions of pendulum-like Hamiltonian systems in the plane. Zbl 1264.34078
2012
Quasistatic crack growth in elasto-plastic materials: the two-dimensional case. Zbl 1304.74005
2010
Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth. Zbl 1419.37059
2019
Quasi-static crack growth in hydraulic fracture. Zbl 1437.74024
Almi, Stefano; Dal Maso, Gianni; Toader, Rodica
2014
Some remarks on the viscous approximation of crack growth. Zbl 1263.74044
2013
Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation. Zbl 1364.49013
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2017
Scaling in fracture mechanics by Bažant law: from finite to linearized elasticity. Zbl 1322.49077
2015
Periodic motions in a gravitational central field with a rotating external force. Zbl 1266.34070
Fonda, Alessandro; Toader, Rodica; Torres, Pedro J.
2012
Quasi-static evolution in brittle fracture: the case of bounded solutions. Zbl 1085.49003
Dal Maso, Gianni; Francfort, Gilles A.; Toader, Rodica
2004
On the Cauchy problem for the wave equation on time-dependent domains. Zbl 1411.35189
2019
Nonlocal approximation of nonisotropic free-discontinuity problems. Zbl 0944.49012
1999
Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition. Zbl 1421.35358
Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica
2019
Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length. Zbl 1318.35008
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2015
On a notion of unilateral slope for the Mumford-Shah functional. Zbl 1119.49017
2007
A note on the integral representation of functionals in the space SBD $$\Omega$$. Zbl 1106.49023
2003
A capacity method for the study of Dirichlet problems for elliptic systems in varying domains. Zbl 0882.35040
1996
A lower semicontinuity result for a free discontinuity functional with a boundary term. Zbl 1379.49010
Almi, Stefano; Dal Maso, Gianni; Toader, Rodica
2017
Scattering in domains with many small obstacles. Zbl 0957.35106
1998
Finite element approximation of non-isotropic free-discontinuity problems. Zbl 0903.49002
1997
On the jerky crack growth in elastoplastic materials. Zbl 1443.74255
2020
Elastodynamic Griffith fracture on prescribed crack paths with kinks. Zbl 1432.35134
Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica
2020
A variational model for the quasi-static growth of fractional dimensional brittle fractures. Zbl 1305.74076
2014
Lower and upper solutions to semilinear boundary value problems: an abstract approach. Zbl 1243.35030
2011
On the jerky crack growth in elastoplastic materials. Zbl 1443.74255
2020
Elastodynamic Griffith fracture on prescribed crack paths with kinks. Zbl 1432.35134
Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica
2020
Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth. Zbl 1419.37059
2019
On the Cauchy problem for the wave equation on time-dependent domains. Zbl 1411.35189
2019
Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition. Zbl 1421.35358
Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica
2019
Rate-independent damage in thermo-viscoelastic materials with inertia. Zbl 1412.35325
Lazzaroni, Giuliano; Rossi, Riccarda; Thomas, Marita; Toader, Rodica
2018
Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation. Zbl 1364.49013
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2017
A lower semicontinuity result for a free discontinuity functional with a boundary term. Zbl 1379.49010
Almi, Stefano; Dal Maso, Gianni; Toader, Rodica
2017
Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case. Zbl 1358.49015
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2016
Scaling in fracture mechanics by Bažant law: from finite to linearized elasticity. Zbl 1322.49077
2015
Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length. Zbl 1318.35008
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
2015
Quasi-static crack growth in hydraulic fracture. Zbl 1437.74024
Almi, Stefano; Dal Maso, Gianni; Toader, Rodica
2014
A variational model for the quasi-static growth of fractional dimensional brittle fractures. Zbl 1305.74076
2014
Some remarks on the viscous approximation of crack growth. Zbl 1263.74044
2013
Periodic solutions of radially symmetric perturbations of Newtonian systems. Zbl 1248.34051
2012
Periodic solutions of singular radially symmetric systems with superlinear growth. Zbl 1251.34056
Fonda, Alessandro; Toader, Rodica; Zanolin, Fabio
2012
Periodic solutions of pendulum-like Hamiltonian systems in the plane. Zbl 1264.34078
2012
Periodic motions in a gravitational central field with a rotating external force. Zbl 1266.34070
Fonda, Alessandro; Toader, Rodica; Torres, Pedro J.
2012
A model for crack propagation based on viscous approximation. Zbl 1277.74066
2011
Radially symmetric systems with a singularity and asymptotically linear growth. Zbl 1218.34047
2011
Periodic orbits of radially symmetric systems with a singularity: the repulsive case. Zbl 1241.34048
2011
Energy release rate and stress intensity factor in antiplane elasticity. Zbl 1228.35243
2011
2011
Lower and upper solutions to semilinear boundary value problems: an abstract approach. Zbl 1243.35030
2011
Quasistatic crack growth in elasto-plastic materials: the two-dimensional case. Zbl 1304.74005
2010
An artificial viscosity approach to quasistatic crack growth. Zbl 1180.35521
2009
Periodic orbits of radially symmetric Keplerian-like systems: a topological degree approach. Zbl 1168.34031
2008
On a notion of unilateral slope for the Mumford-Shah functional. Zbl 1119.49017
2007
Quasistatic crack growth in nonlinear elasticity. Zbl 1064.74150
Dal Maso, Gianni; Francfort, Gilles A.; Toader, Rodica
2005
Quasi-static evolution in brittle fracture: the case of bounded solutions. Zbl 1085.49003
Dal Maso, Gianni; Francfort, Gilles A.; Toader, Rodica
2004
A note on the integral representation of functionals in the space SBD $$\Omega$$. Zbl 1106.49023
2003
A model for the quasi-static growth of brittle fractures: Existence and approximation results. Zbl 1042.74002
2002
A model for the quasi-static growth of brittle fractures based on local minimization. Zbl 1205.74149
2002
A relaxation theorem in the space of functions of bounded deformation. Zbl 0960.49014
Barroso, Ana Cristina; Fonseca, Irene; Toader, Rodica
2000
A density result in SBV with respect to non-isotropic energies. Zbl 0939.49024
1999
Nonlocal approximation of nonisotropic free-discontinuity problems. Zbl 0944.49012
1999
Scattering in domains with many small obstacles. Zbl 0957.35106
1998
Finite element approximation of non-isotropic free-discontinuity problems. Zbl 0903.49002
1997
A capacity method for the study of Dirichlet problems for elliptic systems in varying domains. Zbl 0882.35040
1996
all top 5

#### Cited by 372 Authors

 24 Dal Maso, Gianni 21 Toader, Rodica 17 Mielke, Alexander 15 Fonda, Alessandro 15 Roubíček, Tomáš 14 Rossi, Riccarda 13 Crismale, Vito 13 Lazzaroni, Giuliano 13 Negri, Matteo 10 Chambolle, Antonin 10 Friedrich, Manuel 10 Giacomini, Alessandro 10 Thomas, Marita 9 Larsen, Christopher J. 8 Chu, Jifeng 8 Conti, Sergio 8 Focardi, Matteo 8 Francfort, Gilles A. 8 Solombrino, Francesco 8 Stefanelli, Ulisse 8 Zanini, Chiara 7 Almi, Stefano 7 Cagnetti, Filippo 7 Khludnev, Aleksandr Mikhaĭlovich 7 Liang, Zaitao 7 Ponsiglione, Marcello 7 Sfecci, Andrea 6 Babadjian, Jean-François 6 Braides, Andrea 6 Iurlano, Flaviana 6 Knees, Dorothee 6 Li, Shengjun 6 Marigo, Jean-Jacques 6 Nardini, Lorenzo 6 Wick, Thomas 6 Zeppieri, Caterina Ida 5 Garroni, Adriana 5 Ortiz, Michael 4 Bach, Annika 4 Bucur, Dorin 4 Cheng, Zhibo 4 Lemenant, Antoine 4 Miehe, Christian 4 Orlando, Gianluca 4 Rindler, Filip 4 Savaré, Giuseppe 4 Scala, Riccardo 4 Schmidt, Bernd 4 Scilla, Giovanni 4 Torres, Pedro José 3 Alessi, Roberto 3 Bellettini, Giovanni 3 Buttazzo, Giuseppe 3 Caponi, Maicol 3 Caroccia, Marco 3 De Cicco, Virginia 3 Del Piero, Gianpietro 3 DeSimone, Antonio 3 Fiaschi, Alice 3 Garrione, Maurizio 3 Heinemann, Christian 3 Hofacker, Martina 3 Kružík, Martin 3 Liao, Fangfang 3 Lussardi, Luca 3 Mariano, Paolo Maria 3 Mora-Corral, Carlos 3 Mora, Maria Giovanna 3 Negri, Margherita 3 Ortner, Christoph 3 Panagiotopoulos, Christos G. 3 Qian, Dingbian 3 Scardia, Lucia 2 Acanfora, Fausto 2 Alberti, Giovanni 2 Amar, Micol 2 Amster, Pablo 2 Arroyo-Rabasa, Adolfo 2 Artina, Marco 2 Bellieud, Michel 2 Belz, Sandro 2 Benešová, Barbora 2 Bonetti, Elena 2 Boscaggin, Alberto 2 Bourdin, Blaise 2 Carstensen, Carsten 2 De Philippis, Guido 2 Ebobisse, François Bille 2 Fornasier, Massimo 2 Gallo, Anna Chiara 2 Gelli, Maria Stella 2 Goldman, Michael 2 Hatvani, László 2 Henao, Duvan A. 2 Jakabčin, Lukáš 2 Kholmatov, Shokhrukh Yusufovich 2 Kong, Fanchao 2 Kovtunenko, Viktor Anatolievich 2 Kraus, Christiane 2 Li, Yong ...and 272 more Authors
all top 5

#### Cited in 113 Serials

 33 Archive for Rational Mechanics and Analysis 28 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 22 Calculus of Variations and Partial Differential Equations 19 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 18 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 11 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 9 NoDEA. Nonlinear Differential Equations and Applications 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 SIAM Journal on Mathematical Analysis 7 Computer Methods in Applied Mechanics and Engineering 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Journal of Differential Equations 7 Journal of Elasticity 7 Journal of Nonlinear Science 7 Discrete and Continuous Dynamical Systems 7 Advances in Calculus of Variations 6 Journal of Mathematical Analysis and Applications 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Discrete and Continuous Dynamical Systems. Series S 5 Journal of the Mechanics and Physics of Solids 5 Mathematical Methods in the Applied Sciences 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Journal of Functional Analysis 4 Celestial Mechanics and Dynamical Astronomy 4 Continuum Mechanics and Thermodynamics 4 Nonlinear Analysis. Real World Applications 4 Advanced Nonlinear Studies 3 International Journal for Numerical Methods in Engineering 3 Quarterly of Applied Mathematics 3 Journal of Dynamics and Differential Equations 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Boundary Value Problems 3 Journal of Fixed Point Theory and Applications 3 Advances in Nonlinear Analysis 2 Inverse Problems 2 Nonlinearity 2 Mathematische Nachrichten 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Zeitschrift für Analysis und ihre Anwendungen 2 Acta Applicandae Mathematicae 2 Physica D 2 Computational Mechanics 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Scientific Computing 2 Journal of Convex Analysis 2 Journal of Difference Equations and Applications 2 Mathematics and Mechanics of Solids 2 Abstract and Applied Analysis 2 Interfaces and Free Boundaries 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Communications on Pure and Applied Analysis 2 International Journal of Fracture 2 GAMM-Mitteilungen 2 Inverse Problems and Imaging 2 Journal of Function Spaces 1 Acta Mechanica 1 Computers & Mathematics with Applications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 International Journal of Plasticity 1 Journal d’Analyse Mathématique 1 Journal of Computational Physics 1 Journal of Mathematical Physics 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Annales de l’Institut Fourier 1 Applied Mathematics and Optimization 1 Integral Equations and Operator Theory 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Meccanica 1 Monatshefte für Mathematik 1 Results in Mathematics 1 Ricerche di Matematica 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Acta Mathematicae Applicatae Sinica. English Series 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 European Journal of Applied Mathematics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Communications in Numerical Methods in Engineering 1 Electronic Journal of Differential Equations (EJDE) 1 Opuscula Mathematica 1 Journal of Mathematical Fluid Mechanics 1 Acta Mathematica Sinica. English Series 1 Journal of Dynamical and Control Systems 1 Optimization and Engineering 1 Journal of Evolution Equations 1 Archives of Computational Methods in Engineering 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Analysis and Applications (Singapore) 1 Fixed Point Theory 1 Fixed Point Theory and Applications ...and 13 more Serials
all top 5

#### Cited in 31 Fields

 237 Mechanics of deformable solids (74-XX) 170 Calculus of variations and optimal control; optimization (49-XX) 139 Partial differential equations (35-XX) 69 Ordinary differential equations (34-XX) 35 Operator theory (47-XX) 28 Numerical analysis (65-XX) 24 Real functions (26-XX) 22 Mechanics of particles and systems (70-XX) 15 Dynamical systems and ergodic theory (37-XX) 8 Computer science (68-XX) 8 Fluid mechanics (76-XX) 7 Measure and integration (28-XX) 6 Classical thermodynamics, heat transfer (80-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Information and communication theory, circuits (94-XX) 5 Functional analysis (46-XX) 5 Operations research, mathematical programming (90-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Potential theory (31-XX) 3 Biology and other natural sciences (92-XX) 2 Differential geometry (53-XX) 2 Statistics (62-XX) 2 Geophysics (86-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX)