The Calderón problem with partial data | Zendy

Johannes Sjöstrand | Zendy

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The Calderón problem with partial data

Author(s) -

Johannes Sjöstrand

Publication year - 2008

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.9

Subject(s) - dimension (graph theory) , mathematics , set (abstract data type) , cauchy distribution , dirichlet boundary condition , work (physics) , cauchy boundary condition , dirichlet distribution , boundary (topology) , boundary value problem , cauchy problem , pure mathematics , mathematical analysis , initial value problem , computer science , physics , quantum mechanics , programming language

In this paper we improve an earlier result by Bukhgeim and Uhlmann, by showing that in dimension larger than or equal to three, the knowledge of the Cauchy data for the Schr\"odinger equation measured on possibly very small subsets of the boundary determines uniquely the potential. We follow the general strategy of Bukhgeim and Uhlmann but use a richer set of solutions to the Dirichlet problem.

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