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Monotonicity formulas for obstacle problems with Lipschitz coefficients
Matteo Focardi, Emanuele Spadaro and Maria Stella Gelli
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.