Vol. 6, No. 7, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Other MSP Journals
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