Calculus of Variations and Geometric Measure Theory
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M. Focardi - F. Geraci - E. Spadaro

Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications

created by focardi on 08 Jun 2018

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Submitted Paper

Inserted: 8 jun 2018
Last Updated: 8 jun 2018

Year: 2018

Abstract:

We establish Weiss' and Monneau's type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space $W^{1,p}$, $p>n$, and provide an application to the corresponding free boundary analysis for the related classical obstacle problems.

Keywords: Classical obstacle problem, free boundary, monotonicity formulas


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