Viscosity solutions of fully nonlinear second-order elliptic partial differential equations

Ishii, Hitoshi; Lions, Pierre-Louis

Ishii, Hitoshi; Lions, Pierre-Louis (1990), Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, Journal of Differential Equations, 83, 1, p. 26-78. http://dx.doi.org/10.1016/0022-0396(90)90068-Z

Type

Article accepté pour publication ou publié

Date

1990

Nom de la revue

Journal of Differential Equations

Volume

Numéro

Éditeur

Elsevier

Pages

26-78

Identifiant publication

http://dx.doi.org/10.1016/0022-0396(90)90068-Z

Métadonnées

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Auteur(s)

Ishii, Hitoshi

Lions, Pierre-Louis
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Résumé (EN)

We investigate comparison and existence results for viscosity solutions of fully nonlinear, second-order, elliptic, possibly degenerate equations. These results complement those recently obtained by R. Jensen and H. Ishii. We consider various boundary conditions like for instance Dirichlet and Neumann conditions. We also apply these methods and results to quasilinear Monge-Ampère equations. Finally, we also address regularity questions.

Mots-clés

PDE