Oberseminar Analysis

 

Dienstag, 09.02.2016, 14:15 Uhr

An epiperimetric inequality for the thin obstacle problem

Emanuele Spadaro, MPI MIS Leipzig

Abstract: I will discuss some recent results on the thin obstacle problem (also known as the scalar Signori problem). This is a classical problem in the calculus of variations and, in its simplest form, it consists in minimizing the Dirichlet energy among all functions that are constrained to have a positive trace on a hyperplane. Despite the long tradition, many questions concerning the regularity of the solutions remain still open. In this talk, our focus is on the rate of converge of the solutions to their unique blowup limits near certain points of the free boundary. Following the pioneering work by G. Weiss on the classical obstacle problem, we prove an "epiperimetric inequality" a la Reifenberg, which closely resembles the one firstly shown in the '60s in the study of the regularity of minimal
surfaces. This is a joint work with M. Focardi of the University of Florence.

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Ort: Seminarraum 001, Erdgeschoss,  Pontdriesch 14-16 , 52062 Aachen