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## Alvarez, Olivier

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 Author ID: alvarez.olivier Published as: Alvarez, O.; Alvarez, Olivier
 Documents Indexed: 22 Publications since 1994, including 1 Book
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#### Co-Authors

 1 single-authored 6 Bardi, Martino 5 Monneau, Régis 2 Carlini, Elisabetta 2 Hoch, Philippe 2 Le Bouar, Yann 2 Marchi, Claudio 2 Rouy, Elisabeth 1 Cardaliaguet, Pierre 1 Koike, Shigeaki 1 Nakayama, Isao 1 Tourin, Agnès
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#### Serials

 2 Archive for Rational Mechanics and Analysis 2 SIAM Journal on Control and Optimization 1 Journal of Differential Equations 1 Memoirs of the American Mathematical Society 1 Numerische Mathematik 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Applied Numerical Mathematics 1 Differential and Integral Equations 1 Interfaces and Free Boundaries 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
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#### Fields

 10 Partial differential equations (35-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Numerical analysis (65-XX) 1 Ordinary differential equations (34-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistical mechanics, structure of matter (82-XX)

#### Citations contained in zbMATH

21 Publications have been cited 388 times in 281 Documents Cited by Year
Convex viscosity solutions and state constraints. Zbl 0890.49013
Alvarez, O.; Lasry, J.-M.; Lions, P.-L.
1997
Viscosity solutions of nonlinear integro-differential equations. Zbl 0870.45002
Alvarez, Olivier; Tourin, Agnès
1996
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Zbl 1209.35001
Alvarez, Olivier; Bardi, Martino
2010
Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result. Zbl 1032.35103
Alvarez, Olivier; Bardi, Martino
2003
Viscosity solutions methods for singular perturbations in deterministic and stochastic control. Zbl 1017.49028
Alvarez, Olivier; Bardi, Martino
2001
Dislocation dynamics: Short-time existence and uniqueness of the solution. Zbl 1158.74335
Alvarez, Olivier; Hoch, Philippe; Bouar, Yann Le; Monneau, Régis
2006
Existence and uniqueness for dislocation dynamics with nonnegative velocity. Zbl 1099.35148
Alvarez, O.; Cardaliaguet, P.; Monneau, R.
2005
Hopf-Lax formulas for semicontinuous data. Zbl 0939.35045
Alvarez, O.; Barron, E. N.; Ishii, H.
1999
Multiscale problems and homogenization for second-order Hamilton-Jacobi equations. Zbl 1133.35005
Alvarez, Olivier; Bardi, Martino; Marchi, Claudio
2007
Ergodic problems in differential games. Zbl 1153.91346
Alvarez, Olivier; Bardi, Martino
2007
Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem. Zbl 0949.49020
Alvarez, Olivier; Koike, Shigeaki; Nakayama, Isao
2000
A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics. Zbl 1103.65100
Alvarez, O.; Carlini, E.; Monneau, R.; Rouy, E.
2006
Small-time solvability of a non-local Hamilton-Jacobi equation describing dislocation dynamics. Zbl 1049.35005
Alvarez, Olivier; Hoch, Philippe; Le Bouar, Yann; Monneau, Régis
2004
Hamilton-Jacobi equations with partial gradient and application to homogenization. Zbl 1014.49021
Alvarez, O.; Ishii, H.
2001
Homogenization of Hamilton-Jacobi equations in perforated sets. Zbl 0945.35010
Alvarez, O.
1999
Convergence of a first order scheme for a nonlocal eikonal equation. Zbl 1100.65072
Alvarez, O.; Carlini, E.; Monneau, R.; Rouy, E.
2006
Homogenization in $$L^\infty$$. Zbl 1023.35010
Alvarez, O.; Barron, E. N.
2002
A quasilinear elliptic equation in $$\mathbb{R}^ N$$. Zbl 0859.35010
Alvarez, O.
1996
Bounded from below viscosity solutions of Hamilton-Jacobi equations. Zbl 0890.35026
Alvarez, Olivier
1997
Multiscale singular perturbations and homogenization of optimal control problems. Zbl 1206.93072
Alvarez, O.; Bardi, M.; Marchi, C.
2008
Ergodic control in $$L^\infty$$. Zbl 0968.49018
Alvarez, O.; Barron, E. N.
2000
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Zbl 1209.35001
Alvarez, Olivier; Bardi, Martino
2010
Multiscale singular perturbations and homogenization of optimal control problems. Zbl 1206.93072
Alvarez, O.; Bardi, M.; Marchi, C.
2008
Multiscale problems and homogenization for second-order Hamilton-Jacobi equations. Zbl 1133.35005
Alvarez, Olivier; Bardi, Martino; Marchi, Claudio
2007
Ergodic problems in differential games. Zbl 1153.91346
Alvarez, Olivier; Bardi, Martino
2007
Dislocation dynamics: Short-time existence and uniqueness of the solution. Zbl 1158.74335
Alvarez, Olivier; Hoch, Philippe; Bouar, Yann Le; Monneau, Régis
2006
A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics. Zbl 1103.65100
Alvarez, O.; Carlini, E.; Monneau, R.; Rouy, E.
2006
Convergence of a first order scheme for a nonlocal eikonal equation. Zbl 1100.65072
Alvarez, O.; Carlini, E.; Monneau, R.; Rouy, E.
2006
Existence and uniqueness for dislocation dynamics with nonnegative velocity. Zbl 1099.35148
Alvarez, O.; Cardaliaguet, P.; Monneau, R.
2005
Small-time solvability of a non-local Hamilton-Jacobi equation describing dislocation dynamics. Zbl 1049.35005
Alvarez, Olivier; Hoch, Philippe; Le Bouar, Yann; Monneau, Régis
2004
Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result. Zbl 1032.35103
Alvarez, Olivier; Bardi, Martino
2003
Homogenization in $$L^\infty$$. Zbl 1023.35010
Alvarez, O.; Barron, E. N.
2002
Viscosity solutions methods for singular perturbations in deterministic and stochastic control. Zbl 1017.49028
Alvarez, Olivier; Bardi, Martino
2001
Hamilton-Jacobi equations with partial gradient and application to homogenization. Zbl 1014.49021
Alvarez, O.; Ishii, H.
2001
Uniqueness of lower semicontinuous viscosity solutions for the minimum time problem. Zbl 0949.49020
Alvarez, Olivier; Koike, Shigeaki; Nakayama, Isao
2000
Ergodic control in $$L^\infty$$. Zbl 0968.49018
Alvarez, O.; Barron, E. N.
2000
Hopf-Lax formulas for semicontinuous data. Zbl 0939.35045
Alvarez, O.; Barron, E. N.; Ishii, H.
1999
Homogenization of Hamilton-Jacobi equations in perforated sets. Zbl 0945.35010
Alvarez, O.
1999
Convex viscosity solutions and state constraints. Zbl 0890.49013
Alvarez, O.; Lasry, J.-M.; Lions, P.-L.
1997
Bounded from below viscosity solutions of Hamilton-Jacobi equations. Zbl 0890.35026
Alvarez, Olivier
1997
Viscosity solutions of nonlinear integro-differential equations. Zbl 0870.45002
Alvarez, Olivier; Tourin, Agnès
1996
A quasilinear elliptic equation in $$\mathbb{R}^ N$$. Zbl 0859.35010
Alvarez, O.
1996
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#### Cited by 327 Authors

 11 Barles, Guy 11 Cardaliaguet, Pierre 11 Ley, Olivier 11 Monneau, Régis 9 Bardi, Martino 9 Barron, Emmanuel Nicholas 8 Imbert, Cyril 8 Salani, Paolo 8 Topp, Erwin 7 El Hajj, Ahmad 7 Marchi, Claudio 6 Cesaroni, Annalisa 6 Forcadel, Nicolas 6 Ma, Xi-Nan 6 Quincampoix, Marc 6 Tchou, Nicoletta Anna 5 Camilli, Fabio 5 Jensen, Robert R. 5 Mannucci, Paola 5 Souganidis, Panagiotis E. 4 Alvarez, Olivier 4 Chambolle, Antonin 4 Da Lio, Francesca 4 Gaitsgory, Vladimir A. 4 He, Yiran 4 Lee, Ki-Ahm 4 Liu, Qing 4 Loreti, Paola 4 Monteillet, Aurélien 4 Mou, Chenchen 3 Achdou, Yves 3 Bian, Baojun 3 Buckdahn, Rainer 3 Cannarsa, Piermarco 3 Caselles Costa, Vicent 3 Chasseigne, Emmanuel 3 Chen, ChuanQiang 3 Covei, Dragoş-Pătru 3 Crasta, Graziano 3 Fragalà, Ilaria 3 Ghilli, Daria 3 Guan, Pengfei 3 Ishige, Kazuhiro 3 Ishii, Hitoshi 3 Jakobsen, Espen Robstad 3 Jia, Guangyan 3 Jiang, Yi 3 Karlsen, Kenneth Hvistendahl 3 Nour, Chadi 3 Penot, Jean-Paul 3 Pogodaev, Nikolaĭ Il’ich 3 Rossomakhine, Sergey 3 Rouy, Elisabeth 3 Stroffolini, Bianca 3 Świȩch, Andrzej 3 Tran Vinh Hung 2 Alvarez, Orlando 2 Boudjerada, Rachida 2 Briani, Ariela 2 Carlini, Elisabetta 2 Castelpietra, Marco 2 Cerqueti, Roy 2 Daraghmeh, Adnan 2 Dávila, Gonzalo 2 Dragoni, Federica 2 Droniou, Jérôme 2 Feldman, Mikhail 2 Figalli, Alessio 2 Gensbittel, Fabien 2 Hajej, Ahmed 2 Hamadene, Saïd 2 Hartmann, Carsten 2 Hu, Bowen 2 Ivanov, Grigorii E. 2 Khlopin, Dmitriĭ Valer’evich 2 Kim, Inwon Christina 2 Kim, Kwang Ik 2 Kim, Sunghan 2 Kim, Yong-Cheol 2 Koike, Shigeaki 2 La Chioma, Claudia 2 Le Guyader, Carole 2 Lions, Pierre-Louis 2 Ma, Jin 2 Manfredi, Juan J. 2 Mo, Jiaqi 2 Nakayasu, Atsushi 2 Nguyen, Thi Tuyen 2 Novaga, Matteo 2 Park, Hyun Suk 2 Požár, Norbert 2 Prinari, Francesca 2 Qatanani, Naji A. 2 Qian, Xiaosong 2 Quaas, Alexander 2 Rainer, Catherine 2 Renault, Jérôme 2 Salazar, Wilfredo 2 Siconolfi, Antonio 2 Thibault, Lionel ...and 227 more Authors
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#### Cited in 90 Serials

 18 Journal of Differential Equations 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 Archive for Rational Mechanics and Analysis 13 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 11 NoDEA. Nonlinear Differential Equations and Applications 10 Applied Mathematics and Optimization 9 Calculus of Variations and Partial Differential Equations 8 Journal of Mathematical Analysis and Applications 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Communications in Partial Differential Equations 8 Journal de Mathématiques Pures et Appliquées. Neuvième Série 8 Discrete and Continuous Dynamical Systems 7 Transactions of the American Mathematical Society 6 Advances in Mathematics 6 Mathematische Annalen 6 Dynamic Games and Applications 5 Journal of Optimization Theory and Applications 5 SIAM Journal on Control and Optimization 4 Mathematics of Computation 4 Numerische Mathematik 4 Journal of Global Optimization 4 SIAM Journal on Mathematical Analysis 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Applicable Analysis 3 Communications in Mathematical Physics 3 The Annals of Applied Probability 3 Stochastic Processes and their Applications 3 Communications on Pure and Applied Analysis 3 Set-Valued and Variational Analysis 2 Communications on Pure and Applied Mathematics 2 Applied Mathematics and Computation 2 Archiv der Mathematik 2 Journal of Functional Analysis 2 Manuscripta Mathematica 2 Applied Numerical Mathematics 2 Optimization 2 Probability Theory and Related Fields 2 Revista Matemática Iberoamericana 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Numerical Algorithms 2 Potential Analysis 2 Finance and Stochastics 2 Discrete and Continuous Dynamical Systems. Series S 2 Journal of Dynamics and Games 2 Minimax Theory and its Applications 1 Nonlinearity 1 Czechoslovak Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Mathematics of Operations Research 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Rendiconti del Seminario Matematico della Università di Padova 1 Ricerche di Matematica 1 SIAM Journal on Numerical Analysis 1 Systems & Control Letters 1 Zeitschrift für Analysis und ihre Anwendungen 1 Acta Mathematicae Applicatae Sinica. English Series 1 Applied Mathematics Letters 1 Asymptotic Analysis 1 Annals of Operations Research 1 Japan Journal of Industrial and Applied Mathematics 1 Games and Economic Behavior 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Opuscula Mathematica 1 European Journal of Control 1 Journal of Shanghai University 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 International Game Theory Review 1 Journal of Nonlinear Mathematical Physics 1 Differential Equations 1 Quantitative Finance 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Stochastics 1 Journal of Shanghai Jiaotong University (Science) 1 Journal of the Korean Statistical Society 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 ALEA. Latin American Journal of Probability and Mathematical Statistics 1 Analysis & PDE 1 SIAM Journal on Financial Mathematics 1 Matematicheskaya Teoriya Igr i eë Prilozheniya 1 Journal of Computational Dynamics 1 Mathematics
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#### Cited in 31 Fields

 192 Partial differential equations (35-XX) 136 Calculus of variations and optimal control; optimization (49-XX) 48 Systems theory; control (93-XX) 41 Probability theory and stochastic processes (60-XX) 38 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 21 Integral equations (45-XX) 20 Numerical analysis (65-XX) 19 Operator theory (47-XX) 15 Operations research, mathematical programming (90-XX) 14 Mechanics of deformable solids (74-XX) 11 Ordinary differential equations (34-XX) 9 Real functions (26-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Convex and discrete geometry (52-XX) 9 Differential geometry (53-XX) 8 Mechanics of particles and systems (70-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Measure and integration (28-XX) 5 Difference and functional equations (39-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functional analysis (46-XX) 4 Fluid mechanics (76-XX) 4 Biology and other natural sciences (92-XX) 3 Potential theory (31-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX)