Schauder estimates for some perturbation of an infinite dimensional Ornstein-Uhlenbeck operator
type: Item
instance of: scholarly article
title: Schauder estimates for some perturbation of an infinite dimensional Ornstein-Uhlenbeck operator
zbMATH Open document ID: 1287.47036
author: Guiseppe Da Prato
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2013-03-14T00:00:00Z
review text: The author introduces a semilinear elliptic problem in which the leading, linear term is an infinite-dimensional Ornstein-Uhlenbeck-type operator and the nonlinear perturbation satisfies a smoothness assumption (more precisely, it has to be given by a Hilbert-space-valued function that is uniformly continuous and bounded together with its derivatives up to order 3). If the drift term is given by a negative definite operator with trace-class inverse, then the solution to the associated elliptic problem is shown to satisfy some Schauder-type a-priori estimates.
reviewed by: Delio Mugnolo
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 47N30
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 6144737
zbMATH Keywords: Ornstein-Uhlenbeck operators
zbMATH Keywords: Schauder estimates
zbMATH Keywords: elliptic equations with infinitely many variables
MaRDI profile type: Publication
full work available at URL: dcdss.2013.6.637
OpenAlex ID: W2333930446
DOI: 10.3934/DCDSS.2013.6.637
description: scientific article; zbMATH DE number 6144737