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.

Continuity properties of Neumann-to-Dirichlet maps with respect to the H-convergence of the coefficient matrices / L. Rondi. - In: INVERSE PROBLEMS. - ISSN 0266-5611. - 31:4(2015), pp. 045002.1-045002.24. [10.1088/0266-5611/31/4/045002]

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

L. Rondi
2015

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.
H-convergence; G-convergence; inverse conductivity problem
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/597749
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