Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein - Uhlenbeck semigroup
type: Item
instance of: scholarly article
title: Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein - Uhlenbeck semigroup
zbMATH Open document ID: 1189.35363
DOI: 10.4171/RLM/558
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2010-04-23T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/journal.php
review text: In the very interesting paper under review, the author considers the elliptic equation \[ \lambda \varphi - L\varphi = f, \] where \(\lambda > 0,\) \(f\) is \(\theta \)-Hölder continuous and \(L\) is an Ornstein--Uhlenbeck operator over a Hilbert space \(H.\) The main result asserts that the mapping \(D^{2}\varphi\) (with values in the space of Hilbert--Schmidt operators in \(H\)) is \(\theta\)-Hölder continuous.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5700399
zbMATH Keywords: PDEs with infinitely many variables
zbMATH Keywords: Schauder estimates
zbMATH Keywords: Ornstein--Uhlenbeck semigroup
author: Guiseppe Da Prato
MaRDI profile type: Publication
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OpenAlex ID: W2071995863
description: scientific article; zbMATH DE number 5700399