4 papers
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…
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…
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…
The classical obstacle problem for nonlinear variational energies
Matteo Focardi, Francesco Geraci, Emanuele Spadaro
We develop the complete free boundary analysis for solutions to classical obstacle problems related to nondegenerate nonlinear variational energies. The key tools are optimal $C^{1…