Displaying similar documents to “Anisotropic inverse problems and Carleman estimates”

The Calderón problem with partial data

Johannes Sjöstrand (2004)

Journées Équations aux dérivées partielles

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We describe a joint work with C.E. Kenig and G. Uhlmann [] where we improve an earlier result by Bukhgeim and Uhlmann [], by showing that in dimension n ≥ 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 [] but use a richer set of solutions to the Dirichlet problem.

Boundary value problems and layer potentials on manifolds with cylindrical ends

Marius Mitrea, Victor Nistor (2007)

Czechoslovak Mathematical Journal

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We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators...

30 Years of Calderón’s Problem

Gunther Uhlmann (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.