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Minimal regularity of the solution of some boundary value problems of Signorini's type in polygonal domains

✍ Scribed by Denis Mercier; Serge Nicaise

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
152 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We study the regularity in Sobolev spaces of the solution of transmission problems in a polygonal domain of the plane, with unilateral boundary conditions of Signorini's type in a part of the boundary and Dirichlet or Neumann boundary conditions on the remainder part. We use a penalization method combined with an appropriated lifting argument to get uniform estimates of the approximated solutions in order to obtain some minimal regularity results for the exact solution. The same method allows us to consider problems with thin obstacles. It can be easily extended to 3D problems. (Β© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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