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DC Field | Value | Language |
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dc.contributor.author | Dipierro, Serena | - |
dc.contributor.author | Ros, Xavier | - |
dc.contributor.author | Serra, Joaquim | - |
dc.contributor.author | Valdinoci, Enrico | - |
dc.date.accessioned | 2023-02-24T08:41:04Z | - |
dc.date.available | 2024-06-04T05:10:11Z | - |
dc.date.issued | 2022-06-04 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194122 | - |
dc.description.abstract | We study solutions to $L u=f$ in $\Omega \subset \mathbb{R}^n$, being $L$ the generator of any, possibly nonsymmetric, stable Lévy process. On the one hand, we study the regularity of solutions to $L u=f$ in $\Omega, u=0$ in $\Omega^c$, in $C^{1, \alpha}$ domains $\Omega$. We show that solutions $u$ satisfy $u / d^\gamma \in C^{\varepsilon_0}(\bar{\Omega})$, where $d$ is the distance to $\partial \Omega$, and $\gamma=\gamma(L, \nu)$ is an explicit exponent that depends on the Fourier symbol of operator $L$ and on the unit normal $v$ to the boundary $\partial \Omega$. On the other hand, we establish new integration by_parts identities in half spaces for such operators. These new identities extend previous ones for the fractional Laplacian, but the non-symmetric setting presents some new interesting features. Finally, we generalize the integration by parts identities in half spaces to the case of bounded $C^{1, \alpha}$ domains. We do it via a new efficient approximation argument, which exploits the Hölder regularity of $u / d^\gamma$. This new approximation argument is interesting, we believe, even in the case of the fractional Laplacian. | - |
dc.format.extent | 68 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Elsevier B.V. | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1016/j.aim.2022.108321 | - |
dc.relation.ispartof | Advances in Mathematics, 2022, vol. 401 | - |
dc.relation.uri | https://doi.org/10.1016/j.aim.2022.108321 | - |
dc.rights | cc-by-nc-nd (c) Elsevier B.V., 2022 | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Equacions diferencials | - |
dc.subject.classification | Processos estocàstics | - |
dc.subject.classification | Operadors pseudodiferencials | - |
dc.subject.other | Differential equations | - |
dc.subject.other | Stochastic processes | - |
dc.subject.other | Pseudodifferential operator | - |
dc.title | Non-symmetric stable operators: regularity theory and integration by parts | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 719155 | - |
dc.date.updated | 2023-02-24T08:41:04Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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