Continuity properties of Neumann-to-Dirichlet maps with respect to the $H$-convergence of the coefficient matrices

Abstract

We investigate the continuity of boundary operators, such as the Neumann-to-Dirichlet map, with respect to the coefficient matrices of the underlying elliptic equations. We show that for nonsmooth coefficients the correct notion of convergence is the one provided by $H$-convergence (or $G$-convergence for symmetric matrices). We prove existence results for minimum problems associated to variational methods used to solve the so-called inverse conductivity problem, at least if we allow the conductivities to be anisotropic. In the case of isotropic conductivities we show that on certain occasions existence of a minimizer may fail.

To appear in Inverse Problems

References in corpus (1)

• Uniqueness in Calderon's problem with Lipschitz conductivities

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