Inserted: 16 may 2016
Last Updated: 2 sep 2017
Journal: Annali di Matematica Pura ed Applicata
Doi: DOI: 10.1007/s10231-017-0692-x
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 continuity property. These formulae are used to obtain the regularity of free-boundary points following the approaches by Caffarelli, Monneau and Weiss.