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arXiv · 1411.1978

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

Luca Rondi
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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 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.

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Luca Rondi. 2014-11-07. Continuity properties of Neumann-to-Dirichlet maps with respect to the $H$-convergence of the coefficient matrices. https://doi.org/10.1088/0266-5611%2F31%2F4%2F045002

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