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

2017/08/30 by Knopova, Victoria, Schilling, René L.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.09458

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 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.

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