2019
DOI: 10.1515/acv-2018-0083
|View full text |Cite
|
Sign up to set email alerts
|

Harnack inequality and an asymptotic mean-value property for the Finsler infinity-Laplacian

Abstract: In this paper, we prove a Harnack inequality for nonnegative viscosity supersolutions of nonhomogeneous equations associated with normalized Finsler infinity-Laplace operators. Viscosity solutions to homogeneous equations are also characterized via an asymptotic mean-value property, understood in a viscosity sense.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
1
0
1

Year Published

2020
2020
2024
2024

Publication Types

Select...
5
1

Relationship

0
6

Authors

Journals

citations
Cited by 6 publications
(2 citation statements)
references
References 39 publications
0
1
0
1
Order By: Relevance
“…Laplace方程边值问题解的可微性 [9]。Rosset在用p-laplace 逼近的方法研究了非齐次无穷Laplace方程边值问题解凸 集上解的水平集的凸性及对称性 [10],洪探究了非齐次无 穷Laplace方程的边界可微性 [11],Mebrate和Mohammed 证明了非齐次Finsler无穷Laplace方程的Harnack不等式和 均值原理 [12],冯和洪研究了非齐次无穷Laplace方程在凸 区域的梯度估计和边界可微性 [13],Koch、张和周研究了 非齐次无穷Laplace方程在平面上的Sobolev正则性 [14]。 本文重点研究非齐次规范无穷Laplace方程解的边界 正则性。规范无穷Laplace算子的一般形式为…”
Section: Introductionunclassified
“…Laplace方程边值问题解的可微性 [9]。Rosset在用p-laplace 逼近的方法研究了非齐次无穷Laplace方程边值问题解凸 集上解的水平集的凸性及对称性 [10],洪探究了非齐次无 穷Laplace方程的边界可微性 [11],Mebrate和Mohammed 证明了非齐次Finsler无穷Laplace方程的Harnack不等式和 均值原理 [12],冯和洪研究了非齐次无穷Laplace方程在凸 区域的梯度估计和边界可微性 [13],Koch、张和周研究了 非齐次无穷Laplace方程在平面上的Sobolev正则性 [14]。 本文重点研究非齐次规范无穷Laplace方程解的边界 正则性。规范无穷Laplace算子的一般形式为…”
Section: Introductionunclassified
“…Bibliographical note. In recent years asymptotic mean value formulas characterizing classical or viscosity solutions to linear and nonlinear second order Partial Differential Equations have been proved by many authors; we refer to[6,12,11,8,5,10,7,13,3]. In those papers one can find quite exhaustive bibliography on this subject.…”
mentioning
confidence: 99%