Continuity properties of Neumann-to-Dirichlet maps with respect to the H-convergence of the coefficient matrices. (26th February 2015)

• Record Type: Journal Article
• Authors: Rondi, Luca
• Is Part Of: Inverse problems. Volume 31:Number 4(2015:Apr.)
• Publication Date: 2015-02-26
• Subjects: H-convergence -- G-convergence -- inverse conductivity problem; Primary 49J45 -- Secondary 35R30; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/4/045002
• Languages: English
• ISSNs: 0266-5611

Abstract

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.