Nous donnons une preuve alternative, basée sur lʼéquation de Monge–Ampère du résultat de Dacorogna et Moser (1990) [4] sur la résolution avec la régularité optimale du problème de Dirichlet pour lʼéquation du Jacobien prescrit.
We give an alternative proof, based on the Monge–Ampère equation, of Dacorogna and Moserʼs result (Dacorogna and Moser, 1990) [4] on the solvability with optimal regularity of the Dirichlet problem for the prescribed Jacobian equation.
Accepté le :
Publié le :
Guillaume Carlier 1 ; Bernard Dacorogna 2
@article{CRMATH_2012__350_7-8_371_0,
author = {Guillaume Carlier and Bernard Dacorogna},
title = {R\'esolution du probl\`eme de {Dirichlet} pour l'\'equation du {Jacobien} prescrit via l'\'equation de {Monge{\textendash}Amp\`ere}},
journal = {Comptes Rendus. Math\'ematique},
pages = {371--374},
publisher = {Elsevier},
volume = {350},
number = {7-8},
year = {2012},
doi = {10.1016/j.crma.2012.04.005},
language = {fr},
}
TY - JOUR AU - Guillaume Carlier AU - Bernard Dacorogna TI - Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère JO - Comptes Rendus. Mathématique PY - 2012 SP - 371 EP - 374 VL - 350 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2012.04.005 LA - fr ID - CRMATH_2012__350_7-8_371_0 ER -
%0 Journal Article %A Guillaume Carlier %A Bernard Dacorogna %T Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère %J Comptes Rendus. Mathématique %D 2012 %P 371-374 %V 350 %N 7-8 %I Elsevier %R 10.1016/j.crma.2012.04.005 %G fr %F CRMATH_2012__350_7-8_371_0
Guillaume Carlier; Bernard Dacorogna. Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 371-374. doi : 10.1016/j.crma.2012.04.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.005/
[1] Polar factorization and monotone rearrangement of vector-valued functions, Communications on Pure and Applied Mathematics, Volume 44 (1991), pp. 375-417
[2] Boundary regularity of maps with convex potentials II, Ann. of Math., Volume 144 (1996), pp. 453-496
[3] The Pullback Equation for Differential Forms, PNLDE Series, vol. 83, Birkhaüser, New York, 2012
[4] On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire, Volume 7 (1990), pp. 1-26
[5] Shape recognition via Wasserstein distance, Quart. Appl. Math., Volume 58 (2000), pp. 705-737
[6] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977
[7] On the regularity of the polar factorization for time dependent maps, Calc. Var. Partial Differential Equations, Volume 22 (2005), pp. 343-374
[8] On manifolds homeomorphic to the 7-sphere, Ann. of Math., Volume 64 (1956), pp. 399-405
[9] On the second boundary value problem for equations of Monge–Ampère type, J. Reine Angew. Math., Volume 487 (1997), pp. 115-124
- Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs, Advances in Mathematics, Volume 415 (2023), p. 39 (Id/No 108869) | DOI:10.1016/j.aim.2023.108869 | Zbl:1540.47086
- A least-squares method for the solution of the non-smooth prescribed Jacobian equation, Journal of Scientific Computing, Volume 93 (2022) no. 1, p. 32 (Id/No 15) | DOI:10.1007/s10915-022-01968-8 | Zbl:1497.65222
- The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces, Calculus of Variations and Partial Differential Equations, Volume 60 (2021) no. 1, p. 15 (Id/No 55) | DOI:10.1007/s00526-021-01931-9 | Zbl:1460.35074
- Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with
- An alternating direction method of multipliers for the numerical solution of a fully nonlinear partial differential equation involving the Jacobian determinant, SIAM Journal on Scientific Computing, Volume 40 (2018) no. 1, p. a52-a80 | DOI:10.1137/16m1094075 | Zbl:1380.65363
- The pullback equation, Vector-valued partial differential equations and applications. Cetraro, Italy, July 8–12, 2013, Cham: Springer; Florence: Fondazione CIME, 2017, pp. 1-72 | DOI:10.1007/978-3-319-54514-1_1 | Zbl:1382.35078
- Solution of the Dirichlet problem for the prescribed Jacobian equation by the Monge-Ampère equation, Actes du colloque “EDP-Normandie”, Le Havre, France, Octobre 23–24, 2012, [s.l.]: Fédération Normandie-Mathématiques, 2013, pp. 25-33 | Zbl:1311.35129
Cité par 7 documents. Sources : zbMATH
Commentaires - Politique