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.
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页码：991 / 1006
页数：16
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