Parameter-elliptic and parabolic pseudodifferential boundary problems in global \(L_ p\) Sobolev spaces
type: Item
instance of: scholarly article
title: Parameter-elliptic and parabolic pseudodifferential boundary problems in global \(L_ p\) Sobolev spaces
zbMATH Open document ID: 0877.35142
DOI: 10.1007/BF02571889
author: Gerd Grubb
published in: Mathematische Zeitschrift
publication date: 1997-12-08T00:00:00Z
full work available at URL: https://eudml.org/doc/174714
review text: The results of this paper extend those of the author [Functional calculus of pseudodifferential boundary problems, Birkhäuser, Boston (1986; Zbl 0622.35001)] from the \(L^2\) framework to \(L^p\) Sobolev spaces. More generally, a parameter-dependent pseudodifferential calculus is presented for Besov and Bessel potential spaces, containing as a special case the resolvent construction for an elliptic pseudodifferential boundary value problem. The resolvent considerations are then used to establish solvability results for parabolic initial-boundary value problems of the type \[ \partial_tu+ P_\Omega u+Gu=f\quad\text{for }(x,t)\in\Omega\times I, \] \[ Tu=\varphi\quad\text{for }(x,t)\in\partial\Omega\times I,\quad u|_{t=0}= u_0\quad\text{for }x\in\Omega \] in anisotropic global \(L^p\) spaces.
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 46N20
zbMATH DE Number: 737161
zbMATH Keywords: resolvent construction
zbMATH Keywords: elliptic pseudodifferential boundary value problems
zbMATH Keywords: solvability results for parabolic initial-boundary value problem
reviewed by: Luigi Rodino
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 737161