Optimal regularity for the Signorini problem

Guillen, Nestor
December 2009
Calculus of Variations & Partial Differential Equations;Dec2009, Vol. 36 Issue 4, p533
Academic Journal
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.


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