Optimal regularity for the Signorini problem

Details Optimal regularity for the Signorini problem Optimal regularity for the Signorini problem

2009-01-05

arxiv.org/abs/0901.0421v1

Mathematics

Analysis of PDEs

15 pages

Scientific paper

We prove under general assumptions that solutions of the thin obstacle or Signorini problem in any space dimension achieve the optimal regularity $C^{1,1/2}$. This improves the known optimal regularity results by allowing the thin obstacle to be defined in an arbitrary $C^{1,\beta}$ hypersurface, $\beta>1/2$, 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.

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