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arXiv · 0901.0421

Optimal regularity for the Signorini problem

Nestor Guillen
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Abstract

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 $C^{1,β}$ 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.

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Nestor Guillen. 2009-01-05. Optimal regularity for the Signorini problem. https://arxiv.org/abs/0901.0421

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