Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions

Jérôme Le Rousseau[1]; Nicolas Lerner[2]

  • [1] MAPMO, UMR CNRS 6628, Route de Chartres, Université d’Orléans B.P. 6759 – 45067 Orléans cedex 2 France
  • [2] Projet analyse fonctionnelle, Institut de Mathématiques de Jussieu, UMR CNRS 7586, Université Pierre-et-Marie-Curie (Paris 6), Boîte 186 - 4, Place Jussieu - 75252 Paris cedex 05, France

Journées Équations aux dérivées partielles (2010)

  • page 1-23
  • ISSN: 0752-0360

Abstract

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We consider a second-order selfadjoint 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 moreover prove that the conditions imposed on the weight function are necessary.

How to cite

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Le Rousseau, Jérôme, and Lerner, Nicolas. "Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions." Journées Équations aux dérivées partielles (2010): 1-23. <http://eudml.org/doc/116379>.

@article{LeRousseau2010,
abstract = {We consider a second-order selfadjoint 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 moreover prove that the conditions imposed on the weight function are necessary.},
affiliation = {MAPMO, UMR CNRS 6628, Route de Chartres, Université d’Orléans B.P. 6759 – 45067 Orléans cedex 2 France; Projet analyse fonctionnelle, Institut de Mathématiques de Jussieu, UMR CNRS 7586, Université Pierre-et-Marie-Curie (Paris 6), Boîte 186 - 4, Place Jussieu - 75252 Paris cedex 05, France},
author = {Le Rousseau, Jérôme, Lerner, Nicolas},
journal = {Journées Équations aux dérivées partielles},
keywords = {Carleman estimate; elliptic operator; non-smooth coefficient; sharp condition; quasi-mode},
language = {eng},
month = {6},
pages = {1-23},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions},
url = {http://eudml.org/doc/116379},
year = {2010},
}

TY - JOUR
AU - Le Rousseau, Jérôme
AU - Lerner, Nicolas
TI - Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
JO - Journées Équations aux dérivées partielles
DA - 2010/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 23
AB - We consider a second-order selfadjoint 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 moreover prove that the conditions imposed on the weight function are necessary.
LA - eng
KW - Carleman estimate; elliptic operator; non-smooth coefficient; sharp condition; quasi-mode
UR - http://eudml.org/doc/116379
ER -

References

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  13. J. Le Rousseau, N. Lerner, Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions, in prep. (2010) 
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  15. J. Le Rousseau, L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces, Invent. Math, to appear (2010) Zbl1218.35054
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