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Seminar

HA Postdoc Seminar: Harmonic Measure and Approximating Domains May 12, 2017 (12:00 PM PDT - 12:50 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Simon Bortz (University of Minnesota, Twin Cities)
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In 1977, Dahlberg solved the L^2 Dirichlet problem on Lipschitz domains for the Laplacian. In particular, he showed that harmonic measure is quantitatively mutually absolutely continuous with respect to surface measure. Since this time, several mathematicians have used this result to prove a variety of absolute continuity properties of harmonic measure on rough sets. The key to results of this flavor is constructing "good" approximating Lipschitz domains. In this talk we will sketch why this method works, then we will give a proof that surface measure is absolutely continuous with respect to harmonic measure under some "weak" assumptions.

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