The Dirichlet problem for nonlocal Lévy-type operators
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 existen...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:182690 |
| Acceso en línea: | https://ddd.uab.cat/record/182690 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6211811 |
| Access Level: | acceso abierto |
| Palabra clave: | Dirichlet problem Nonlocal operator Maximum principle Weak solutions Extension operator |
| Sumario: | 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. |
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