An indefinite Laplacian on a rectangle

Jussi Behrndt; David Krejcirik

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arXiv · 1407.7802

An indefinite Laplacian on a rectangle

Jussi Behrndt·David Krejcirik

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Abstract

In this note we investigate the nonelliptic differential expression A=-div sgn grad on a rectangular domain in the plane. The seemingly simple problem to associate a selfadjoint operator with the differential expression A in an L^2 setting is solved here. Such indefinite Laplacians arise in mathematical models of metamaterials characterized by negative electric permittivity and/or negative magnetic permeability.

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BibTeX RIS

Jussi Behrndt, David Krejcirik. 2014-07-29. An indefinite Laplacian on a rectangle. https://arxiv.org/abs/1407.7802

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