Journal d'Analyse Mathématique

, Volume 134, Issue 2, pp 501–522 | Cite as

An indefinite Laplacian on a rectangle

  • Jussi BehrndtEmail author
  • David Krejčiřík


In this note, we investigate the nonelliptic differential expression
$$A = - div\operatorname{sgn} \nabla $$
on a rectangular domain Ω in the plane. The seemingly simple problem of associating a self-adjoint operator with the differential expression A in L2(Ω) 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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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  1. 1.Institut für Numerische MathematikTechnische Universität GrazGrazAustria
  2. 2.Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePrague 2Czech Republic

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