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CNA Working Group Seminar
Laurent Dietrich
CMU
Title: Elliptic problem in varying domains

Abstract: We will study sequences of solutions of an elliptic equation in varying domains. We will start with the case of the Laplacian and domains converging in the sense of Hausdorff, as in this case explicit examples and computations can be conducted. We will see how the notion of capacity arises to tell us if the limiting solution satisfies the limiting equation, or if and how additional terms can appear at the end. I will follow the book of Henrot & Pierre. We will then present a more recent compactness result by Dal Maso and Garroni about arbitrary sequences of subdomains and a general elliptic (possibly non-symmetric) operator where they describe precisely the additional term possibly arising at the end.

Date: Tuesday, February 28, 2017
Time: 2:30 pm
Location: Wean Hall 7218
Submitted by:  Riccardo Cristoferi