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

Hitoshi Ishii*

*この研究の対応する著者

研究成果: Article査読

209 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)15-45
ページ数31
ジャーナルCommunications on Pure and Applied Mathematics
42
1
DOI
出版ステータスPublished - 1989
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

フィンガープリント

「On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル