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 leadin...

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Bibliographic Details
Published inResultate der Mathematik Vol. 75; no. 2
Main Authors Apel, Thomas, Nicaise, Serge
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2020
Springer Verlag
Subjects
Analysis of PDEs
Mathematics
Mathematics and Statistics
35B65
49N60
coincidence set
regularity
Signorini problem
Mathematics Subject Classification. 35B65 49N60 Signorini problem coincidence set regularity
49N60 Signorini problem
Mathematics Subject Classification. 35B65
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ISSN1422-6383
1420-9012
DOI10.1007/s00025-020-01202-7

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Summary: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 / ( 2 α 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.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-020-01202-7