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On uniqueness and existence of viscosity solutions of fully nonlinear second‐order elliptic PDE's
Author(s) -
Ishii Hitoshi
Publication year - 1989
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160420103
Subject(s) - uniqueness , mathematics , degenerate energy levels , nonlinear system , viscosity solution , viscosity , order (exchange) , mathematical analysis , thermodynamics , physics , finance , quantum mechanics , economics
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.