The Calderón problem with partial data
Journées équations aux dérivées partielles (2004), article no. 9, 9 p.

We describe a joint work with C.E. Kenig and G. Uhlmann [9] where we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension n3, the knowledge of the Cauchy data for the Schrödinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of [1] but use a richer set of solutions to the Dirichlet problem.

Nous décrivons un travail avec C.E. Kenig and G. Uhlmann [9] dans lequel nous améliorons un résultat de Bukhgeim and Uhlmann [1], en montrant qu’en dimension n3, la connaissance des données de Cauchy pour l’équation de Schrödinger sur des sous-ensembles possiblement très petits du bord détermine le potential de manière unique. Nous suivons la stratégie générale de [1] mais nous utilisons un ensemble plus riche de solutions du problème de Dirichlet.

DOI : https://doi.org/10.5802/jedp.9
Classification:  35R30
Keywords: Dirichlet to Neumann map, Carleman estimates, analytic microlocal analysis
@article{JEDP_2004____A9_0,
     author = {Sj\"ostrand, Johannes},
     title = {The Calder\'on problem with partial data},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2004},
     doi = {10.5802/jedp.9},
     zbl = {1152.35518},
     mrnumber = {2135364},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2004____A9_0}
}
Sjöstrand, Johannes. The Calderón problem with partial data. Journées équations aux dérivées partielles (2004), article  no. 9, 9 p. doi : 10.5802/jedp.9. http://www.numdam.org/item/JEDP_2004____A9_0/

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