A probabilistic proof of the breakdown of Besov regularity in L-shaped domains
Research output: Contribution to book/conference proceedings/anthology/report › Conference contribution › Contributed › peer-review
Contributors
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
| Original language | English |
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| Title of host publication | Stochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016 |
| Editors | Gerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat |
| Publisher | Springer Verlag, New York |
| Pages | 473-488 |
| Number of pages | 16 |
| ISBN (print) | 9783319749280 |
| Publication status | Published - 2018 |
| Peer-reviewed | Yes |
Publication series
| Series | Springer proceedings in mathematics and statistics |
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| Volume | 229 |
| ISSN | 2194-1009 |
Conference
| Title | International conference on Stochastic Partial Differential Equations and Related Fields 2016 |
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| Abbreviated title | SPDERF 2016 |
| Duration | 10 - 14 October 2016 |
| City | Bielefeld |
| Country | Germany |
Keywords
ASJC Scopus subject areas
Keywords
- Besov regularity, Brownian motion, Conformal mapping, Dirichlet problem, Poisson equation, Stochastic representation