Ryan Gibara (University of Cincinnati)

Title: Sobolev spaces and Dirichlet problems on metric measure spaces

Abstract: In this talk, we will discuss one of the many generalisations of Sobolev functions to the setting of a metric measure space with no a priori smooth structure, the so-called Newton-Sobolev functions. In the setting of a doubling metric measure space supporting a Poincaré inequality, one is then able to study boundary-value problems via a variational characterization. In this talk, we will discuss progress being made on solving the Dirichlet problem in unbounded domains with boundary data in the Besov space. This is based on work with Luca Capogna, Riikka Korte, and Nageswari Shanmugalingam.

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https://us06web.zoom.us/j/83180453914?pwd=RQnoWH7aQqXAxldXZsqdafFCmh7dBC.1

Meeting ID: 831 8045 3914

Passcode: 719821