Besov正则性在$L$型域上失效的一个概率证明
A Probabilistic proof of the breakdown of Besov regularity in $L$-shaped domains
摘要：
{We提供了一种概率方法，以调查光滑的解决方案的泊松和狄利克雷问题的$L$形域。特别是，我们获得（概率）整表示的解决方案。我们还恢复Grisvard的经典结果的角度依赖性故障的规则性的解决方案中测量的Besov规模。
英文摘要：
{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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