Optimal regularity for the Signorini problem
Abstract
Description
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.
15 pages
15 pages