The Dirichlet problem for nonlocal operators
type: Item
instance of: scholarly article
title: The Dirichlet problem for nonlocal operators
zbMATH Open document ID: 1317.47046
author: Matthieu Felsinger
author: Moritz Kassmann
author: Paul Voigt
published in: Mathematische Zeitschrift
publication date: 2015-04-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/1309.5028
review text: The authors consider elliptic and parabolic Dirichlet problems for linear nonlocal operators with known boundary data on the complement of a given bounded set. Unique solvability is obtained in convenient spaces. The method is based on an appropriate combination of nonlocal versions of the Poincaré-Friedrichs inequality, a Gårding inequality, the Lax-Milgram lemma, the weak maximum principle for integro-differential operators in bounded domains, and the Fredholm alternative. Several concrete examples of the used kernels are included and discussed in the final section.
reviewed by: L. P. Castro
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6422641
zbMATH Keywords: integro-differential operator
zbMATH Keywords: nonlocal operator
zbMATH Keywords: fractional Laplacian
zbMATH Keywords: Dirichlet problem
MaRDI profile type: Publication
OpenAlex ID: W1995655627
arXiv ID: 1309.5028
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DOI: 10.1007/S00209-014-1394-3
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description: scientific article