A mean value formula for the variational p-Laplacian

被引：7
|
作者：
del Teso, Felix [1 ]
Lindgren, Erik [2 ]
机构：
[1] Univ Complutense Madrid, Dept Anal Matemat & Matemat Aplicada, Madrid 28040, Spain
[2] Uppsala Univ, Dept Math, Box 480751 06, Uppsala, Sweden
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 28卷 / 03期
基金：
瑞典研究理事会;
关键词：
p-Laplacian; Mean value property; Viscosity solutions; Dynamic programming principle; VISCOSITY SOLUTIONS; VALUE PROPERTY; EQUIVALENCE; WEAK;
D O I：
10.1007/s00030-021-00688-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a new asymptotic mean value formula for the p-Laplace operator, D(p)u = div(vertical bar del u vertical bar(p-2)del u), 1 < p < infinity valid in the viscosity sense. In the plane, and for a certain range of p, the mean value formula holds in the pointwise sense. We also study the existence, uniqueness and convergence of the related dynamic programming principle.
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页数：33
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