Calculus of Variations and Partial Differential Equations

, 36:533

Optimal regularity for the Signorini problem

Article

DOI: 10.1007/s00526-009-0242-5

Cite this article as:
Guillen, N. Calc. Var. (2009) 36: 533. doi:10.1007/s00526-009-0242-5

Abstract

We prove under general assumptions that solutions of the thin obstacle or Signorini problem in any space dimension achieve the optimal regularity C1,1/2. This improves the known optimal regularity results by allowing the thin obstacle to be defined in an arbitrary C1,β hypersurface, β > 1/2, additionally, our proof covers any linear elliptic operator in divergence form with smooth coefficients. The main ingredients of the proof are a version of Almgren’s monotonicity formula and the optimal regularity of global solutions.

Mathematics Subject Classification (2000)

35R3574G40

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA