Analysis Seminar

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An indefinite Laplacian on a rectangle

Speaker: Jussi Behrndt, Technische Universitaet Graz

Location: Warren Weaver Hall 1302

Date: Thursday, March 29, 2018, 11 a.m.

Synopsis:

In this talk we investigate the nonelliptic differential expression 
$-\text{div}\,\text{sgn}\,\nabla$ on a rectangular domain  $\Omega$ in the plane. 
The seemingly simple problem to associate a selfadjoint operator with this differential expression in $L^2(\Omega)$ is solved, and some spectral and approximation properties of this 
operator are discussed. Such indefinite Laplacians arise in mathematical models of metamaterials
characterized by negative electric permittivity and/or negative magnetic permeability.