The Signorini problem for the Laplace operator is considered in a general polygonal domain. It is proved that the coincidence set consists of a finite number of boundary parts plus a finite number of isolated points. The regularity of the solution is described. In particular, we show that the leading singularity is in general $$r_i^{\pi /(2\alpha _i)}$$ r i π / ( 2 α i ) at transition points of Signorini to Dirichlet or Neumann conditions but $$r_i^{\pi /\alpha _i}$$ r i π / α i at kinks of the Signorini boundary, with $$\alpha _i$$ α i being the internal angle of the domain at these critical points.

中文翻译：

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多边形域中标量Signorini问题解的规律性

在一般多边形域中考虑拉普拉斯算子的 Signorini 问题。证明了重合集由有限数量的边界部分加上有限数量的孤立点组成。描述了解的规律性。特别是，我们表明，在 Signorini 到 Dirichlet 或 Neumann 条件的过渡点处，主要奇异点通常为 $$r_i^{\pi /(2\alpha _i)}$$ ri π / ( 2 α i ) r_i^{\pi /\alpha _i}$$ ri π / α i 在 Signorini 边界的扭结处，$$\alpha _i$$ α i 是这些临界点处域的内角。