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MiS Preprint
53/2013

Monotonicity formulas for obstacle problems with Lipschitz coefficients

Matteo Focardi, Emanuele Spadaro and Maria Stella Gelli

Abstract

We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Hölder continuous linear term.

With the help of those formulas we are able to carry out the full analysis of the regularity of free-boundary points following the approaches of Caffarelli, Weiss and Monneau.

Received:
Jun 5, 2013
Published:
Jun 17, 2013

Related publications

inJournal
2015 Repository Open Access
Matteo Focardi, Emanuele Spadaro and Maria Stella Gelli

Monotonicity formulas for obstacle problems with Lipschitz coefficients

In: Calculus of variations and partial differential equations, 54 (2015) 2, pp. 1547-1573