An indefinite Laplacian on a rectangle
Spectral Theory
2018-11-26 v3 Mathematical Physics
Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.1407.7802,
title = {An indefinite Laplacian on a rectangle},
author = {Jussi Behrndt and David Krejcirik},
journal= {arXiv preprint arXiv:1407.7802},
year = {2018}
}
Comments
to appear in Journal d'Analyse Math\'ematique