A probabilistic proof of the breakdown of Besov regularity in L-shaped domains
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Beitragende
Abstract
We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in L-shaped domains. In particular, we obtain (probabilistic) integral representations (9), (12)–(14) for the solution. We also recover Grisvard’s classic result on the angle-dependent breakdown of the regularity of the solution measured in a Besov scale.
Details
| Originalsprache | Englisch |
|---|---|
| Titel | Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 |
| Redakteure/-innen | Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat |
| Herausgeber (Verlag) | Springer Verlag, New York |
| Seiten | 473-488 |
| Seitenumfang | 16 |
| ISBN (Print) | 9783319749280 |
| Publikationsstatus | Veröffentlicht - 2018 |
| Peer-Review-Status | Ja |
Publikationsreihe
| Reihe | Springer proceedings in mathematics and statistics |
|---|---|
| Band | 229 |
| ISSN | 2194-1009 |
Konferenz
| Titel | International conference on Stochastic Partial Differential Equations and Related Fields 2016 |
|---|---|
| Kurztitel | SPDERF 2016 |
| Dauer | 10 - 14 Oktober 2016 |
| Stadt | Bielefeld |
| Land | Deutschland |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Besov regularity, Brownian motion, Conformal mapping, Dirichlet problem, Poisson equation, Stochastic representation