The Calderón problem with partial data

• Autores: Carlos E. Kenig, Johannes Sjöstrand, Gunther Uhlmann
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 165, Nº 2, 2007, págs. 567-591
• Idioma: inglés
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• Resumen

  • In this paper we improve an earlier result by Bukhgeim and Uhlmann [1], by showing that in dimension n . 3, the knowledge of the Cauchy data for the Schr¿Nodinger 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. This implies a similar result for the problem of Electrical Impedance Tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary.