On maximal regularity of type \(L^p-L^q\) under minimal assumptions for elliptic non-divergence operators
type: Item
instance of: scholarly article
title: On maximal regularity of type \(L^p-L^q\) under minimal assumptions for elliptic non-divergence operators
zbMATH Open document ID: 1165.47030
author: Peer Christian Kunstmann
published in: Journal of Functional Analysis
publication date: 2008-12-22T00:00:00Z
review text: For operators of the form \[ A_{q} = \sum_{\mid \alpha \mid \leq m} a_{\alpha} (x) D^{\alpha}, \;\;\;D(A_{q}) = W_{q}^{m} (\mathbb{R}^{n},\mathbb{C}), \] considered in the space \(L^{q} (\mathbb{R}^{n}, \mathbb{C}),\) \((1 < q < \infty),\) the author gives a positive answer to Brézis' question. Namely, if \(A_{q}\) has maximal regularity of type \(L^{p} - L^{q}\), \(1 < p < \infty,\) whenever \(A_{q}\) generates an analytic semigroup in \(L^{q} (\mathbb{R}^{n}, \mathbb{C})\). The methods applied are new and substantially generalize those previously known for operators with bounded measurable coefficients depending on one coordinate only.
reviewed by: Petru A. Cojuhari
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 5480710
zbMATH Keywords: non-divergence form operators
zbMATH Keywords: elliptic operators
zbMATH Keywords: maximal regularity of type \(L^p-L^q\)
zbMATH Keywords: analytic semigroups
zbMATH Keywords: Davies-Gaffney estimates
zbMATH Keywords: off-diagonal bounds
zbMATH Keywords: elliptic regularity
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.09.017
OpenAlex ID: W2116390246
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DOI: 10.1016/J.JFA.2008.09.017
description: scientific article; zbMATH DE number 5480710