Maximal \(L_p\)-regularity of parabolic problems with boundary dynamics of relaxation type
type: Item
instance of: scholarly article
title: Maximal \(L_p\)-regularity of parabolic problems with boundary dynamics of relaxation type
zbMATH Open document ID: 1160.35030
author: Rico Zacher
author: R. Denk
author: Jan Pruess
published in: Journal of Functional Analysis
publication date: 2008-12-22T00:00:00Z
review text: The authors face interesting problems, such as dynamic boundary problems and linearized free boundary value problems in the context of the general theory of vector valued parabolic initial boundary value problems of relaxion type. They are able to get a very general \(L^p\) regularity theory. They use the tool of semigroup theory to get the maximal regularity for some model problems and then they are able to get the required result in the general case. All these results are obtained under the Lopatinskii-Shapiro conditions that the authors prove to be necessary conditions.
reviewed by: Vincenzo Vespri
Mathematics Subject Classification ID: 35K50
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 5480705
zbMATH Keywords: maximal regularity
zbMATH Keywords: parabolic initial boundary value problems
zbMATH Keywords: dynamic boundary conditions
zbMATH Keywords: vector valued Sobolev spaces
zbMATH Keywords: semigroup theory
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.07.012
OpenAlex ID: W2139993731
cites work: Well-posedness of a Two-phase Flow with Soluble Surfactant
cites work: Q4431977
cites work: Q4788740
cites work: ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
cites work: Optimal \(L^{p}\)- \(L^{q}\)-estimates for parabolic boundary value problems with inhomogeneous data
cites work: Quasilinear parabolic systems with dynamical boundary conditions
cites work: Analytic solutions for a Stefan problem with Gibbs-Thomson correction
cites work: On operators with bounded imaginary powers in Banach spaces
cites work: The Cahn-Hilliard equation with dynamic boundary conditions.
cites work: Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
DOI: 10.1016/J.JFA.2008.07.012
description: scientific article; zbMATH DE number 5480705