On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's

Hitoshi Ishii

Research output: Contribution to journalArticle

184 Citations (Scopus)

Abstract

We prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations. One of them extends some recent uniqueness results by Jensen. Some establish the uniqueness of solutions for second‐order Isaacs' equations and hence include the uniqueness results for Bellman equations by P.‐L. Lions. Our comparison results apply even for discontinuous solutions and so Perron's method readily yields the existence of continuous solutions.

Original languageEnglish
Pages (from-to)15-45
Number of pages31
JournalCommunications on Pure and Applied Mathematics
Volume42
Issue number1
DOIs
Publication statusPublished - 1989
Externally publishedYes

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Elliptic PDE
Fully Nonlinear
Viscosity Solutions
Existence and Uniqueness
Uniqueness
Viscosity
Isaacs Equation
Degenerate Elliptic Equations
Bellman Equation
Discontinuous Solutions
Continuous Solution
Uniqueness of Solutions
Comparison Result
Comparison Theorem
Existence Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's. / Ishii, Hitoshi.

In: Communications on Pure and Applied Mathematics, Vol. 42, No. 1, 1989, p. 15-45.

Research output: Contribution to journalArticle

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