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

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
Journal name
Journal of Differential Equations
Volume
83
Number
1
Publisher
Elsevier
Pages
26-78
Publication identifier
Metadata
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Author(s)
Ishii, Hitoshi

Lions, Pierre-Louis
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (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.
Subjects / Keywords
PDE