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

Author： Rondi Luca  

Publisher： IOP Publishing

E-ISSN： 1361-6420|31|4|45002-45025

ISSN： 0266-5611

Source： Inverse Problems, Vol.31, Iss.4, 2015-04, pp. : 45002-45025

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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 with 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.

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