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Mathematical Sciences Faculty and Graduate Research Colloquium - "The Signorini problem with Lipschitz coefficients: optimal regularity and new monotonicity formulas"

Contributed by: Susan Bourne
Published: Thursday, 31 October 2013 5:00 AM
Department of Mathematical Sciences
Faculty and Graduate Research Colloquium
 
“The Signorini problem with Lipschitz coefficients: optimal regularity and new monotonicity formulas”
Mariana Smit Vega Garcia
(Purdue University)
 
Thursday, November 7, 2013
1:00-1:50pm
RB 449
 
Abstract:
 
We will describe the lower-dimensional obstacle problem for a uniformly elliptic, divergence form operator L =  div( A(x) \nabla ) with Lipschitz continuous coefficients and discuss the optimal regularity of the solution. Our main result states that, similarly to what happens when L = \Delta, the variational solution has the optimal interior regularity C^{1,1/2}_{loc}(Omega_{+/-} \cup M), where M is a codimension one flat manifold which supports the obstacle and divides the domain Omega into two parts, Omega_{+} and Omega_{-}. We achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated Almgren's frequency functional. This is joint work with Nicola Garofalo.
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