Regularity of the Solution of the Scalar Signorini Problem in Polygonal Domains

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^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.