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

H. Ishii, P. L. Lions

Research output: Contribution to journalArticle

294 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)26-78
Number of pages53
JournalJournal of Differential Equations
Volume83
Issue number1
DOIs
Publication statusPublished - 1990
Externally publishedYes

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Fully Nonlinear
Elliptic Partial Differential Equations
Viscosity Solutions
Partial differential equations
Boundary conditions
Viscosity
Degenerate Elliptic Equations
Neumann Condition
Dirichlet conditions
Comparison Result
Existence Results
Complement
Regularity

ASJC Scopus subject areas

  • Analysis

Cite this

Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. / Ishii, H.; Lions, P. L.

In: Journal of Differential Equations, Vol. 83, No. 1, 1990, p. 26-78.

Research output: Contribution to journalArticle

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