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

10/01/2019

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by   Thomas Apel, et al.

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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^π/(2α_i) at transition points of Signorini to Dirichlet or Neumann conditions but r_i^π/α_i at kinks of the Signorini boundary, with α_i being the internal angle of the domain at these critical points.