A probabilistic proof of the breakdown of Besov regularity in L-shaped domains

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in KonferenzbandBeigetragenBegutachtung

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

OriginalspracheEnglisch
TitelStochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
Redakteure/-innenGerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
Herausgeber (Verlag)Springer Verlag, New York
Seiten473-488
Seitenumfang16
ISBN (Print)9783319749280
PublikationsstatusVeröffentlicht - 2018
Peer-Review-StatusJa

Publikationsreihe

ReiheSpringer proceedings in mathematics and statistics
Band229
ISSN2194-1009

Konferenz

TitelInternational conference on Stochastic Partial Differential Equations and Related Fields 2016
KurztitelSPDERF 2016
Dauer10 - 14 Oktober 2016
StadtBielefeld
LandDeutschland

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • Besov regularity, Brownian motion, Conformal mapping, Dirichlet problem, Poisson equation, Stochastic representation