Vol. 6, No. 7, 2013

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Carleman estimates for anisotropic elliptic operators with jumps at an interface

Jérôme Le Rousseau and Nicolas Lerner

Vol. 6 (2013), No. 7, 1601–1648
Abstract

We consider a second-order self-adjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight function such that a Carleman estimate holds true. We also prove that the conditions imposed on the weight function are sharp.

Keywords
Carleman estimate, elliptic operator, nonsmooth coefficient, quasimode
Mathematical Subject Classification 2010
Primary: 35J15, 35J57, 35J75
Milestones
Received: 31 January 2012
Revised: 8 March 2013
Accepted: 13 April 2013
Published: 27 December 2013
Authors
Jérôme Le Rousseau
Laboratoire de Mathématiques —Analyse, Probabilités, Modélisation —Orléans
Université d’Orléans
Bâtiment de mathématiques —Route de Chartres
B.P. 6759
45067 Orléans Cedex 2
France
Fédération Denis-Poisson, CNRS FR 2964 Institut Universitaire de France
Nicolas Lerner
Institut de Mathématiques de Jussieu
Université Pierre et Marie Curie (Paris VI)
Boîte 186
4 Pl. Jussieu
75252 Paris Cedex 5
France