Solvability of linear local and nonlocal Robin problems over \(C (\overline {\varOmega})\)
type: Item
instance of: scholarly article
title: Solvability of linear local and nonlocal Robin problems over \(C (\overline {\varOmega})\)
zbMATH Open document ID: 1242.35116
author: Alejandro Vélez-Santiago
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-11-02T00:00:00Z
review text: This paper is concerned with solvability of linear local and nonlocal Robin problems over \(C(\overline {\varOmega})\), where \(\Omega \subseteq \mathbb R^N\) is a bounded Lipschitz domain. Firstly, the author considers an elliptic boundary value problem with general Robin boundary conditions. The boundary conditions can be either local or nonlocal, depending on the conditions imposed on the elliptic operator. He proves that this boundary value problem is uniquely solvable, and moreover he shows that such weak solution is Hölder continuous on \(\overline {\varOmega}\). He also proves that a realization of the associated differential operator with generalized local or nonlocal Robin boundary conditions generates an analytic \(C_{0}\)-semigroup of angle \(\pi /2\) over \(C(\overline {\varOmega})\). He concludes by applying the elliptic regularity theory to solve the corresponding Cauchy problem over \(C(\overline {\varOmega})\).
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 5966294
zbMATH Keywords: local and nonlocal Robin boundary conditions
zbMATH Keywords: Feller resolvent
zbMATH Keywords: inverse positivity
zbMATH Keywords: analytic \(C_{0}\)-semigroup
zbMATH Keywords: local and nonlocal Cauchy problem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.08.028
OpenAlex ID: W2016647890
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DOI: 10.1016/J.JMAA.2011.08.028
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description: scientific article; zbMATH DE number 5966294