Calculus of Variations and Geometric Measure Theory

M. Colombo - L. Spolaor - B. Velichkov

A logarithmic epiperimetric inequality for the obstacle problem

created by velichkov on 07 Aug 2017
modified on 21 Apr 2018


Accepted Paper

Inserted: 7 aug 2017
Last Updated: 21 apr 2018

Journal: Geom. Funct. Anal.
Year: 2017


For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23–50). In particular, at singular points we introduce a new tool, which we call logarithmic epiperimetric inequality, which yields an explicit logarithmic modulus of continuity on the $C^1$ regularity of the singular set, thus improving previous results of Caffarelli and Monneau.