Calculus of Variations and Geometric Measure Theory

M. Focardi - M. S. Gelli - E. Spadaro

Monotonicity formulas for obstacle problems with Lipschitz coefficients

created by focardi on 14 May 2013
modified on 26 Feb 2015


Published Paper

Inserted: 14 may 2013
Last Updated: 26 feb 2015

Journal: Calc. Var. Partial Differential Equations
Year: 2015
Doi: 10.1007/s00526-015-0835-0


We prove quasi-monotonicity formulas for classical obstacle-type problems with energies being the sum of a quadratic form with Lipschitz coefficients, and a Holder 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 by Caffarelli, Monneau and Weiss.