An indefinite Laplacian on a rectangle
  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. 
Jussi Behrndt and David Krejcirik
math.SP math-ph math.AP math.MP