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

Victoria Knopova; René L. Schilling

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arXiv · 1708.09458

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

Victoria Knopova·René L. Schilling

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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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Victoria Knopova, René L. Schilling. 2017-09-17. A Probabilistic proof of the breakdown of Besov regularity in $L$-shaped domains. https://arxiv.org/abs/1708.09458

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