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

H. Ishii, P. L. Lions

Research output: Contribution to journalArticle

305 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

ASJC Scopus subject areas

  • Analysis

Fingerprint Dive into the research topics of 'Viscosity solutions of fully nonlinear second-order elliptic partial differential equations'. Together they form a unique fingerprint.

  • Cite this