The Dirichlet problem for nonlocal Lévy-type operators
Rutkowski, Artur (Wroclaw University of Science and Technology (Wroclaw, Polònia). Faculty of Pure and Applied Mathematics)

Date:	2018
Abstract:	We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric Lévy processes whose Lévy measures need not be absolutely continuous. We establish basic facts about the Sobolev spaces for such operators, in particular we prove the existence and uniqueness of weak solutions. We present strong and weak variants of maximum principle, and L∞ bounds for solutions. We also discuss the related extension problem in C1,1 domains.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Dirichlet problem ; Nonlocal operator ; Maximum principle ; Weak solutions ; Extension operator
Published in:	Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 213-251 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/329968
DOI: 10.5565/PUBLMAT6211811

39 p, 494.2 KB

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