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Continuity properties of Neumann-to-Dirichlet maps with respect to the $H$-convergence of the coefficient matrices
- Source :
- Inverse Problems 31 (4) (2015) 045002
- Publication Year :
- 2014
-
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.<br />Comment: To appear in Inverse Problems
- Subjects :
- Mathematics - Analysis of PDEs
Primary 49J45, Secondary 35R30
Subjects
Details
- Database :
- arXiv
- Journal :
- Inverse Problems 31 (4) (2015) 045002
- Publication Type :
- Report
- Accession number :
- edsarx.1411.1978
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/0266-5611/31/4/045002