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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.
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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 $\mathbb{R}^n$ ...
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35J15 ; 35J08 ; 31A15