Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Journées équations aux dérivées partielles (2010), article no. 13, 23 p.

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.

DOI : https://doi.org/10.5802/jedp.70
Mots clés : Carleman estimate; elliptic operator; non-smooth coefficient; sharp condition; quasi-mode
@article{JEDP_2010____A13_0,
     author = {Le Rousseau, J\'er\^ome and Lerner, Nicolas},
     title = {Carleman estimates for elliptic operators with jumps at an interface: {Anisotropic} case and sharp geometric conditions},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {13},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2010},
     doi = {10.5802/jedp.70},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jedp.70/}
}
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Le Rousseau, Jérôme; Lerner, Nicolas. Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions. Journées équations aux dérivées partielles (2010), article  no. 13, 23 p. doi : 10.5802/jedp.70. http://archive.numdam.org/articles/10.5802/jedp.70/

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