Strong Maximum Principle and Boundary Estimates for Nonhomogeneous Elliptic Equations

被引：2

作者：

Lundstroem, Niklas L. P. ^{[1
]}

Olofsson, Marcus ^{[1
]}

Toivanen, Olli ^{[2
]}

机构：

[1] Umea Univ, Dept Math & Math Stat, SE-90187 Umea, Sweden

[2] Univ Eastern Finland, Dept Appl Phys, FI-70210 Kuopio, Finland

来源：

POTENTIAL ANALYSIS | 2024年 / 60卷 / 01期

基金：

瑞典研究理事会;

关键词：

Osgood condition; Non-Lipschitz drift; Non-standard growth; Variable exponent; Fully nonlinear; Sphere condition; Laplace equation; Hopf Lemma; Boundary Harnack inequality; P-HARMONIC-FUNCTIONS; VISCOSITY SOLUTIONS; HARNACK PRINCIPLE; DIFFERENTIAL-EQUATIONS; POSITIVE SOLUTIONS; MARTIN BOUNDARY; BEHAVIOR; LIPSCHITZ; PROPAGATION; INEQUALITY;

D O I：

10.1007/s11118-022-10055-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear nonhomogeneous degenerate elliptic equations on the form F(x, u, Du, D(2)u) = 0 under suitable assumptions allowing for non-Lipschitz growth in the gradient term. In case of smooth boundaries, we also prove a Hopf lemma, a boundary Harnack inequality, and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply, e.g., to weak solutions of an eigenvalue problem for the variable exponent p-Laplacian.

引用

页码：425 / 443

页数：19

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