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.
Titolo: | Continuity properties of Neumann-to-Dirichlet maps with respect to the H-convergence of the coefficient matrices |
Autori: | RONDI, LUCA (Corresponding) |
Parole Chiave: | H-convergence; G-convergence; inverse conductivity problem |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Data di pubblicazione: | 2015 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/0266-5611/31/4/045002 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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