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math.AP2018
Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications
Matteo Focardi, Francesco Geraci, Emanuele Spadaro
We establish Weiss' and Monneau's type quasi-monotonicity formulas for quadratic energies having matrix of coefficients in a Sobolev space , , and provide an applicat…
math.AP2017
The Classical Obstacle problem with coefficients in fractional Sobolev spaces
Francesco Geraci
We prove quasi-monotonicity formulae for classical obstacle-type problems with quadratic energies with coefficients in fractional Sobolev spaces, and a linear term with a Dini-type…
math.AP2017
An epiperimetric inequality for the lower dimensional obstacle problem
Francesco Geraci
In this paper we give a proof of an epiperimetric inequality in the setting of the lower dimensional obstacle problem. The inequality was introduced by Weiss (Invent. Math., 138 (1…