Dirichlet problem for sets with higher co-dimensional boundaries.
The PDE & Analysis seminar covers topics in PDE and analysis.
Date & time
Date/time
9 Sep 2022 | 12 - 1pm
Speaker
Speakers
Joseph Feneuil, ANU
Event series
Event series
Contact
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Description
Abstract:
For a given bounded domain $\Omega$ with non-tengential access to its boundary, the Dirichlet problem (for the Laplacian) is solvable if and only if the boundary is uniformly rectifiable. In this talk, I shall first present this nice result linking geometry and PDE, and we will discuss the literature surrounding it. Together with Guy David and Svitlana Mayboroda, we aim to extend this characterization of uniform rectifiability to the low dimension. I will talk about our strategy, the results that we successfully extended in low dimension, as well as the differences with the above classical case.
Location
Seminar Room 1.33
Hanna Neumann Building 145
Science Road
Action 2601
-35.275387198178, 149.11925554276