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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
16/2015

An epiperimetric inequality for the thin obstacle problem

Matteo Focardi and Emanuele Spadaro

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.

Received:
25.02.15
Published:
25.03.15
MSC Codes:
35R35
Keywords:
Epiperimetric inequality, Thin obstacle problem, Regularity of the free boundary

Related publications

inJournal
2016 Repository Open Access
Matteo Focardi and Emanuele Spadaro

An epiperimetric inequality for the thin obstacle problem

In: Advances in differential equations, 21 (2016) 1/2, pp. 153-200