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

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.

13 pages, 4 figures