On the stochastic \(p\)-Laplace equation
type: Item
instance of: scholarly article
title: On the stochastic \(p\)-Laplace equation
zbMATH Open document ID: 1180.60055
author: Wei Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-11-06T00:00:00Z
review text: The \(p\)-Laplace equation with random perturbation \[ dX_t=\left[\text{div}\left(|\nabla X_t|^{p-2}\nabla X_t\right) -\gamma |X_t|^{p-2}\right]dt + BdW_t, \quad X_0=x \] in the singular case \(1<p\leq 2\) where \(\gamma\geq 0\), \(B\) is a Hilbert-Schmidt operator and \(W\) a cylindrical Brownian motion is studied. Some ergodicity, ultraboundedness and compactness properties for the associated transition semigroups are obtained. Moreover, uniqueness of the invariant measure and convergence rate of the semigroup are derived. The main tool is a dimension-free Harnack inequality which is established by a coupling argument. Results are applied to stochastic reaction-diffusion equations and stochastic \(p\)-Laplace equations in Hilbert space.
reviewed by: Franco Fagnola
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35K92
zbMATH DE Number: 5626948
zbMATH Keywords: \(p\)-Laplace equation
zbMATH Keywords: Harnack inequality
zbMATH Keywords: strong Feller property
zbMATH Keywords: irreducibility
zbMATH Keywords: transition semigroup
zbMATH Keywords: ultraboundedness
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.07.020
OpenAlex ID: W2171185408
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DOI: 10.1016/J.JMAA.2009.07.020
description: scientific article; zbMATH DE number 5626948