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arXiv · 1708.02045

A logarithmic epiperimetric inequality for the obstacle problem

Maria Colombo·Luca Spolaor·Bozhidar Velichkov
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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 $C^1$ regularity of the singular set, thus improving previous results of Caffarelli and Monneau.

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Maria Colombo, Luca Spolaor, Bozhidar Velichkov. 2017-08-07. A logarithmic epiperimetric inequality for the obstacle problem. https://arxiv.org/abs/1708.02045

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