The Calderón problem with partial data

Sjöstrand, Johannes

Journées équations aux dérivées partielles (2004), article no. 9, 9 p.

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 $n\ge 3$, 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.

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 $n\ge 3$, 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.

Classification : 35R30
Mots clés : Dirichlet to Neumann map, Carleman estimates, analytic microlocal analysis

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