Partial Cauchy data for general second order elliptic operators in two dimensions

By Oleg Yu. Imanuvilov, Gunther Uhlmann, Masahiro Yamamoto. 2010

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We consider the problem of determining the coefficients of a first-order perturbation of the Laplacian in two dimensions by measuring the corresponding Cauchy data on an arbitrary open subset of the boundary. From this information we obtain a coupled system of ∂z and ∂z which the coefficients satisfy. As a corollary we show that for a simply connected domain we can determine uniquely the coefficients up to the natural obstruction. Another consequence of our result is that the magnetic field and the electric potential are uniquely determined by measuring the partial Cauchy data associated to the magnetic Schrodinger equation measured on an arbitrary open subset of the boundary. of the boundary. We also show that the coefficients of any real vector field perturbation of the Laplacian, the convection terms, are uniquely determined by their partial Cauchy data.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d264dbc6dea9607832669164edb2dc7a5681d8ca

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In Applied Mathematics

In Computational Theory and Mathematics

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Citations in the corpus

Inverse problems for elliptic equations with power type nonlinearities (2019, background): “J∗g,σ−1J∗q = ΛJ(M1),g,q where J and σ satisfy boundary conditions as above. For the linear equation ∆gu + qu = 0, an analogous result has been proved when M is a domain in R2 with a Riemannian metric [IUY12], when M is a manifold and the potentials are zero [LU01], and when the manifold M is a prior”