Analysis and Probability seminar

Abstract: In this talk we will present the Robin harmonic measure and how it behaves on non smooth domains. In particular we will prove that, in contrast with respect to the Dirichlet case, Robin harmonic measure is quantitatively mutually absolutely continuous with respect to the surface measure on any Ahlfors regular set in any (quantifiably) connected domain for any elliptic operator. This stands in contrast with analogous results for the Dirichlet boundary value problem where rectifiability  is necessary in order to have mutual absolute continuity. Moreover Robin harmonic measures exhibit no dimension drop that is a classical phenomenon in the Dirichlet counterpart.

This is a joint work with: Guy David, Stefano Decio, Max Engelstein and Svitlana Mayboroda.