An epiperimetric inequality for the thin obstacle problem

Matteo Focardi and Emanuele Spadaro

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Submission date: 25. Feb. 2015
Pages: 38
published in: Advances in differential equations, 21 (2016) 1/2, p. 153-200 
Bibtex
MSC-Numbers: 35R35
Keywords and phrases: Epiperimetric inequality, Thin obstacle problem, Regularity of the free boundary
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Abstract:
We prove an epiperimetric inequality for the thin obstacle problem, thus extending the pioneering results by Weiss on the classical obstacle problem (Invent. Math. 138 (1999), no. 1, 23-50). This inequality provides the means to study the rate of converge of the rescaled solutions to their limits, as well as the regularity properties of the free boundary.