A logarithmic epiperimetric inequality for the obstacle problem
Analysis of PDEs
2017-08-08 v1
Abstract
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 regularity of the singular set, thus improving previous results of Caffarelli and Monneau.
Cite
@article{arxiv.1708.02045,
title = {A logarithmic epiperimetric inequality for the obstacle problem},
author = {Maria Colombo and Luca Spolaor and Bozhidar Velichkov},
journal= {arXiv preprint arXiv:1708.02045},
year = {2017}
}