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Carleman estimates for
anisotropic elliptic operators with jumps at an interface
Jérôme Le Rousseau and Nicolas Lerner |
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Vol. 6 (2013), No. 7, 1601–1648
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 35J15, 35J57, 35J75
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Milestones
Received: 31 January 2012
Revised: 8 March 2013
Accepted: 13 April 2013
Published: 27 December 2013
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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 |
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