An Epiperimetric Inequality for the Thin Obstacle problem

26 Feb 2015 · Focardi Matteo, Spadaro Emanuele ·

We prove an epiperimetric inequality for the thin obstacle problem, 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.