An epiperimetric inequality for the thin obstacle problem
Matteo Focardi and Emanuele Spadaro
Contact the author: Please use for correspondence this email.
Submission date: 25. Feb. 2015
published in: Advances in differential equations, 21 (2016) 1/2, p. 153-200
Keywords and phrases: Epiperimetric inequality, Thin obstacle problem, Regularity of the free boundary
Download full preprint: PDF (544 kB)
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.