On the stochastic p-Laplace equation

被引：17

作者：

Liu, Wei ^{[1
,2
]}

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[2] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 360卷 / 02期

关键词：

p-Laplace equation; Harnack inequality; Strong Feller property; Irreducibility; Transition semigroup; Ultraboundedness; PARTIAL-DIFFERENTIAL-EQUATIONS; GENERALIZED POROUS-MEDIA; FAST-DIFFUSION-EQUATIONS; NAVIER-STOKES EQUATIONS; HARNACK INEQUALITY; FUNCTIONAL INEQUALITIES; SOBOLEV INEQUALITIES; TIME ASYMPTOTICS; MANIFOLDS; ERGODICITY;

D O I：

10.1016/j.jmaa.2009.07.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The p-Laplace equation with random perturbation is studied for the singular case 1 < p <= 2 in this paper. Some properties of the invariant measure and transition semigroups are obtained. The main tool is the dimension-free Harnack inequality, which is established by using the coupling argument. As consequences, some ergodicity, compactness and contractive properties are derived for. the associated transition semigroups. The main results are applied to stochastic reaction-diffusion equations and the stochastic p-Laplace equation in Hilbert space. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：737 / 751

页数：15

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