# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 26 Publications since 1997
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#### Co-Authors

 5 single-authored 11 Lewicka, Marta , Wang, Dehua 3 Mora, Maria Giovanna 2 Liu, Zhuomin 2 Mahadevan, Lakshminarayanan 2 Müller, Stefan 1 Acharya, Amit 1 Goldstein, Paweł 1 Hajłasz, Piotr 1 Hornung, Peter 1 Jerrard, Robert Leon 1 Jullien, Alexandra 1 Keshavarz, Mehdi 1 Lloyd, J. L. 1 Malý, Jan 1 Ochoa, Pablo D. 1 Pakzad, R. 1 Phillips, C. R. jun. 1 Plas, F. 1 Rivière, Tristan 1 Robinet, Jean-Christophe
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#### Serials

 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Archive for Rational Mechanics and Analysis 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Nonlinearity 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Differential Geometry 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annals of Global Analysis and Geometry 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Parallel Computing 1 Differential and Integral Equations 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Calculus of Variations and Partial Differential Equations 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Contemporary Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Analysis & PDE 1 Journal of Fuzzy Set Valued Analysis
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#### Fields

 12 Mechanics of deformable solids (74-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Partial differential equations (35-XX) 6 Differential geometry (53-XX) 5 Functional analysis (46-XX) 3 Functions of a complex variable (30-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Computer science (68-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

23 Publications have been cited 306 times in 148 Documents Cited by Year
On the Sobolev space of isometric immersions. Zbl 1064.58009
2004
Scaling laws for non-Euclidean plates and the $$W^{2,2}$$ isometric immersions of Riemannian metrics. Zbl 1300.74028
2011
The Föppl-von Kármán equations for plates with incompatible strains. Zbl 1219.74027
2011
Weak density of smooth maps for the Dirichlet energy between manifolds. Zbl 1028.58008
2003
Shell theories arising as low energy $$\Gamma$$-limit of 3d nonlinear elasticity. Zbl 1425.74298
2010
The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. Zbl 1291.74130
2011
Regularity properties of isometric immersions. Zbl 1082.58010
2005
The infinite hierarchy of elastic shell models: some recent results and a conjecture. Zbl 1263.74035
2012
Convergence of equilibria of thin elastic plates – the von Kármán case. Zbl 1141.74034
2008
Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells. Zbl 1322.74049
2013
The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells. Zbl 1359.35085
2017
Convex integration for the Monge-Ampère equation in two dimensions. Zbl 1370.35151
2017
Variational models for prestrained plates with Monge-Ampère constraint. Zbl 1363.74063
2015
A nonlinear theory for shells with slowly varying thickness. Zbl 1168.74036
2009
Weak density of smooth maps in $$W^{1, 1}(M,N)$$ for non-Abelian $${\pi}_1(N)$$. Zbl 1040.58002
2003
Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension. Zbl 1375.35235
2017
Rigidity and regularity of co-dimension one Sobolev isometric immersions. Zbl 1337.58007
2015
Independent columns: A new parallel ILU preconditioner for the PCG method. Zbl 0907.68030
Pakzad, M.; Lloyd, J. L.; Phillips, C.
1997
Finite distortion Sobolev mappings between manifolds are continuous. Zbl 1457.58005
2019
The metric-restricted inverse design problem. Zbl 1342.74099
2016
Relaxing the Dirichlet energy for maps into $$S^2$$ in high dimensions. Zbl 1012.58013
2002
Existence of infinitely many weakly harmonic maps from a domain in $$\mathbb{R}^n$$ into $$S^2$$ for non-constant boundary data. Zbl 0993.58008
2001
A general modelling of expansive and non-expansive clays. Zbl 0944.74593
Robinet, J. C.; Pakzad, M.; Jullien, A.; Plas, F.
1999
Finite distortion Sobolev mappings between manifolds are continuous. Zbl 1457.58005
2019
The Monge-Ampère constraint: matching of isometries, density and regularity, and elastic theories of shallow shells. Zbl 1359.35085
2017
Convex integration for the Monge-Ampère equation in two dimensions. Zbl 1370.35151
2017
Sobolev spaces of isometric immersions of arbitrary dimension and co-dimension. Zbl 1375.35235
2017
The metric-restricted inverse design problem. Zbl 1342.74099
2016
Variational models for prestrained plates with Monge-Ampère constraint. Zbl 1363.74063
2015
Rigidity and regularity of co-dimension one Sobolev isometric immersions. Zbl 1337.58007
2015
Infinitesimal isometries on developable surfaces and asymptotic theories for thin developable shells. Zbl 1322.74049
2013
The infinite hierarchy of elastic shell models: some recent results and a conjecture. Zbl 1263.74035
2012
Scaling laws for non-Euclidean plates and the $$W^{2,2}$$ isometric immersions of Riemannian metrics. Zbl 1300.74028
2011
The Föppl-von Kármán equations for plates with incompatible strains. Zbl 1219.74027
2011
The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. Zbl 1291.74130
2011
Shell theories arising as low energy $$\Gamma$$-limit of 3d nonlinear elasticity. Zbl 1425.74298
2010
A nonlinear theory for shells with slowly varying thickness. Zbl 1168.74036
2009
Convergence of equilibria of thin elastic plates – the von Kármán case. Zbl 1141.74034
2008
Regularity properties of isometric immersions. Zbl 1082.58010
2005
On the Sobolev space of isometric immersions. Zbl 1064.58009
2004
Weak density of smooth maps for the Dirichlet energy between manifolds. Zbl 1028.58008
2003
Weak density of smooth maps in $$W^{1, 1}(M,N)$$ for non-Abelian $${\pi}_1(N)$$. Zbl 1040.58002
2003
Relaxing the Dirichlet energy for maps into $$S^2$$ in high dimensions. Zbl 1012.58013
2002
Existence of infinitely many weakly harmonic maps from a domain in $$\mathbb{R}^n$$ into $$S^2$$ for non-constant boundary data. Zbl 0993.58008
2001
A general modelling of expansive and non-expansive clays. Zbl 0944.74593
Robinet, J. C.; Pakzad, M.; Jullien, A.; Plas, F.
1999
Independent columns: A new parallel ILU preconditioner for the PCG method. Zbl 0907.68030
Pakzad, M.; Lloyd, J. L.; Phillips, C.
1997
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#### Cited by 147 Authors

 18 Hornung, Peter 14 Lewicka, Marta , Wang, Dehua 9 Pakzad, Mohammad Reza 8 Mora, Maria Giovanna 7 Velčić, Igor 6 Kupferman, Raz 6 Mucci, Domenico 6 Müller, Stefan 5 Giaquinta, Mariano 5 Maor, Cy 4 Bousquet, Pierre 4 Harutyunyan, Davit 4 Isobe, Takeshi 4 Olbermann, Heiner 4 Tambača, Josip 4 Van Schaftingen, Jean 3 Agostiniani, Virginia 3 Conti, Sergio 3 Davoli, Elisa 3 DeSimone, Antonio 3 Hardt, Robert M. 3 Liu, Zhuomin 3 Malý, Jan 3 Marohnić, Maroje 3 Neukamm, Stefan 3 Ponce, Augusto C. 3 Rivière, Tristan 3 Schmidt, Bernd 3 Shachar, Asaf 3 Yao, Pengfei 2 Abels, Helmut 2 Ball, John M. 2 Bartels, Sören 2 Bethuel, Fabrice 2 Bhattacharya, Kaushik 2 Canevari, Giacomo 2 Cicalese, Marco 2 Dolzmann, Georg 2 Hajłasz, Piotr 2 Jiménez Bolaños, Silvia 2 Kohn, Robert Vita 2 Maggiani, Giovanni Battista 2 Orlandi, Giandomenico 2 Raoult, Annie 2 Ruf, Matthias 2 Schäffner, Mathias 2 Solombrino, Francesco 2 Venkataramani, Shankar C. 2 Zarnescu, Arghir Dani 1 Acharya, Amit 1 Arroyo, Marino 1 Audoly, Basile 1 Bauer, Robert Otto 1 Bella, Peter 1 Blanchard, Dominique 1 Brubaker, Nicholas D. 1 Brunetti, Matteo 1 Bufford, Laura 1 Cao, Wentao 1 Chen, Yichao 1 Cherdantsev, Mikhail 1 Cherednichenko, Kirill D. 1 Chermisi, Milena 1 Chow, Edmond G. W. 1 Christowiak, Fabian 1 Class, Holger 1 Codenotti, Luca 1 Dall’Acqua, Anna 1 Delgado, Miguel de Benito 1 Eberhard, Peter 1 Efrati, Efi 1 Ehlers, Wolfgang 1 Favata, Antonino 1 Focardi, Matteo 1 Fonseca, Irene 1 Freddi, Lorenzo 1 Freiboth, Sandra 1 Fried, Eliot 1 Friedrich, Manuel 1 Friesecke, Gero 1 Gemmer, John A. 1 Goldstein, Paweł 1 Grabovsky, Yury 1 Graf, Tobias 1 Griso, Georges 1 Hang, Fengbo 1 Helmig, Rainer 1 James, Richard D. 1 Jerrard, Robert Leon 1 Kim, Seonghak 1 Koh, Youngwoo 1 Koumatos, Konstantinos 1 Kreisbeck, Carolin 1 Krömer, Stefan 1 Kružík, Martin 1 Lai, Baishun 1 Lecumberry, Myriam 1 Lega, J. 1 Lemm, Marius 1 Lestringant, Claire ...and 47 more Authors
all top 5

#### Cited in 55 Serials

 19 Calculus of Variations and Partial Differential Equations 18 Archive for Rational Mechanics and Analysis 16 Journal of Elasticity 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Journal of Functional Analysis 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 SIAM Journal on Mathematical Analysis 4 Journal of Nonlinear Science 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Mathematische Zeitschrift 3 Mathematics and Mechanics of Solids 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Analysis & PDE 2 Journal of the Mechanics and Physics of Solids 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Acta Mathematica 2 Annals of Global Analysis and Geometry 2 The Journal of Geometric Analysis 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Mathematische Annalen 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Numerische Mathematik 1 Zeitschrift für Analysis und ihre Anwendungen 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 Applied Mathematics Letters 1 Differential Geometry and its Applications 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 Communications in Partial Differential Equations 1 SIAM Journal on Scientific Computing 1 Computational Geosciences 1 Engineering Computations 1 Communications in Contemporary Mathematics 1 Journal of Systems Science and Complexity 1 Communications on Pure and Applied Analysis 1 GAMM-Mitteilungen 1 Journal of Fixed Point Theory and Applications 1 Advances in Calculus of Variations 1 Confluentes Mathematici 1 Science China. Mathematics 1 Evolution Equations and Control Theory 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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#### Cited in 23 Fields

 102 Mechanics of deformable solids (74-XX) 46 Partial differential equations (35-XX) 43 Calculus of variations and optimal control; optimization (49-XX) 29 Differential geometry (53-XX) 25 Global analysis, analysis on manifolds (58-XX) 20 Functional analysis (46-XX) 7 Numerical analysis (65-XX) 5 Fluid mechanics (76-XX) 4 Algebraic topology (55-XX) 3 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX)