SOLUTIONS TO A CLASS OF PARABOLIC INHOMOGENEOUS NORMALIZED p-LAPLACE EQUATIONS

被引：0

作者：

Liu, Fang ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Sci, Dept Appl Math, Nanjing 210094, Jiangsu, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2015年 / 35卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Parabolic normalized p-Laplace equation; viscosity solution; asymptotic mean value property; comparison principle; uniqueness theorem; infinity Laplacian; TUG-OF-WAR; MEAN-VALUE CHARACTERIZATION; VISCOSITY SOLUTIONS; INFINITY;

D O I：

10.1016/S0252-9602(15)60016-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we prove that viscosity solutions of the parabolic inhomogeneous equations n + p/p u(t) - Delta(N)(p) u = f(x, t) can be characterized using asymptotic mean value properties for all p >= 1, including p = 1 and p = infinity. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.

引用

页码：477 / 494

页数：18

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