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arXiv · 1910.00228

Regularity of the solution of the scalar Signorini problem in polygonal domains

Thomas Apel·Serge Nicaise
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Abstract

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 isolated points. The regularity of the solution is described. In particular, we show that the leading singularity is in general $r_i^{\pi/(2\alpha_i)}$ at transition points of Signorini to Dirichlet or Neumann conditions but $r_i^{\pi/\alpha_i}$ at kinks of the Signorini boundary, with $\alpha_i$ being the internal angle of the domain at these critical points.

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Thomas Apel, Serge Nicaise. 2019-10-01. Regularity of the solution of the scalar Signorini problem in polygonal domains. https://arxiv.org/abs/1910.00228

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