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

Hitoshi Ishii

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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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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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