Abstract : Joint work with Stefano Decio, Max Engelstein, Mario Michetti, and Svitlana Mayboroda. The Robin boundary condition is $\frac{1}{a} \frac{\partial u}{\partial n}+u=f$ on the boundary of a domain $U$, and we claim that for $0< a< +\infty$, the corresponding harmonic measure is mutually absolutely continuous with respect to surface measure. Here (we hope we will have finished checking that) we can consider any bounded domain $U$ in $\mathbb{R}^n$ whose boundary is Ahlfors regular of dimension $d$, $n-2< d< n$, with nontangential access. The Robin condition is then to be taken weakly, and surface measure becomes Hausdorff measure.

Keywords : Robin boundary condition; harmonic measure