analysis of partial differential equations

Robin harmonic measure with a variable permeability parameter

arXiv:2510.22354

summary

The paper investigates solutions to the Robin boundary value problem on bounded one-sided NTA domains with Ahlfors‑David regular boundaries, extending previous results to the case where the Robin (permeability) parameter varies, and shows that the resulting Robin harmonic measure is mutually absolutely continuous with surface measure.

Abstract

In this paper we study the behavior of the solutions to the Robin problem in bounded -sided NTA domains with Ahlfors-David regular boundary, generalizing the results of \cite{DavDEMM} to the case of a non constant Robin parameter. In particular, we will prove the mutual absolute continuity of the Robin harmonic measure with respect to the surface measure in the setting of variable permeability.

34 pages

Topics & keywords

#robin boundary condition#harmonic measure#variable permeability#nta domains#ahlfors-david regularity#absolute continuityRobin problemharmonic measurevariable Robin parameterNTA domainAhlfors‑David regularmutual absolute continuity
Robin harmonic measure with a variable permeability parameter · wovepaper