BZ Seminar in Analysis: Svitlana Mayboroda (ETH Zürich)

Free boundary problems for the partially reflected Brownian motion: dimension of the Robin harmonic measure

We construct the harmonic measure associated to partially reflective Brownian motion (that is, Robin boundary data) and demonstrate that its behavior is surprisingly different from the Dirichlet analogue. In particular, contrary to the traditional setting and to some predictions in physics literature, it is absolutely continuous with respect to the Hausdorff measure for a large class of operators and domains. 

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