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 , 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 , 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.
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}, eid = {9}, pages = {1--9}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2004}, doi = {10.5802/jedp.9}, mrnumber = {2135364}, zbl = {1152.35518}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.9/} }
TY - JOUR AU - Sjöstrand, Johannes TI - The Calderón problem with partial data JO - Journées équations aux dérivées partielles PY - 2004 SP - 1 EP - 9 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.9/ DO - 10.5802/jedp.9 LA - en ID - JEDP_2004____A9_0 ER -
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/articles/10.5802/jedp.9/
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