Monotonicity formulas for obstacle problems with Lipschitz coefficients

Matteo Focardi, Emanuele Spadaro, and Maria Stella Gelli

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Submission date: 05. Jun. 2013
Pages: 25
published in: Calculus of variations and partial differential equations, 54 (2015) 2, p. 1547-1573 
DOI number (of the published article): 10.1007/s00526-015-0835-0
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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.