Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. I: Convex operators

被引：21

作者：

Bardi, M ^{[1
]}

Da Lio, F ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35131 Padua, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2001年 / 44卷 / 08期

关键词：

propagation of maxima; hopf boundary lemma; strong maximum principle; fully nonlinear pdes; degenerate elliptic equations; Hamilton-Jacobi-Bellman equations; semicontinuous viscosity subsolutions;

D O I：

10.1016/S0362-546X(99)00317-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An appropriate extension of all the subsolutions of fully nonlinear degenerate elliptic equations F(x,u(x), Du(x),D2u(x)) = 0 (1.2) in ω, under the assumption that F is convex in the (u,Du,D2) variables is given. Since the degenerate equations of form (1.2) do not have classical solutions in general, the framework of viscosity solutions is derived.

引用

页码：991 / 1006

页数：16

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