| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 39 | |
| Number of page(s) | 33 | |
| DOI | https://doi.org/10.1051/cocv/2018024 | |
| Published online | 20 September 2019 | |
An epiperimetric inequality for the lower dimensional obstacle problem
DiMaI, Università degli studi di Firenze,
Viale Morgagni 67/A,
50134
Firenze, Italy.
* Corresponding author: geraci@math.unifi.it
Received:
4
September
2017
Accepted:
5
April
2018
In this paper we give a proof of an epiperimetric inequality in the setting of the lower dimensional obstacle problem. The inequality was introduced by Weiss [Invent. Math. 138 (1999) 23–50) for the classical obstacle problem and has striking consequences concerning the regularity of the free-boundary. Our proof follows the approach of Focardi and Spadaro [Adv. Differ. Equ. 21 (2015) 153–200] which uses an homogeneity approach and a Γ-convergence analysis.
Mathematics Subject Classification: 35R35
Key words: Epiperimetric inequality / lower dimensional obstacle problem / free-boundary / Γ-convergence
© EDP Sciences, SMAI 2019
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