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Nonlinear Analysis

The insulated conductivity problem and the maximum principle

Ben Weinkove, Northwestern University

Location:  Hill Center Room 705
Date & time: Tuesday, 11 October 2022 at 1:40PM - 2:40PM

Abstract: Harmonic functions in narrow regions with Neumann boundary conditions are used to model the electric potential in the presence of insulating inclusions a short distance apart. The gradient of the harmonic function - the electric field - may blow up as the inclusions approach each other. Optimal estimates for the electric field were recently obtained by Dong-Li-Yang. I will discuss a maximum principle approach to this problem, known as the insulated conductivity problem.

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