Some non-linear systems of PDEs related to inverse problems in conductivity
type: Item
instance of: scholarly article
title: Some non-linear systems of PDEs related to inverse problems in conductivity
zbMATH Open document ID: 1472.35008
author: Faustino Maestre
author: Pablo Pedregal
published in: Calculus of Variations and Partial Differential Equations
publication date: 2021-06-04T00:00:00Z
review text: The main focus of the article is the Euler-Lagrange system associated with the functional \[ I(u) = \int_{\Omega} |\nabla u_1| |\nabla u_2| \mathrm{d} x. \] This gives a system of PDEs with a connection to the Calderón's problem: the conductivity will be \[ \gamma = \frac{\|\nabla u_2\|}{\|\nabla u_1\|}. \] The functional is non-coercive and not quasiconvex, foiling the direct method in calculus of variations. The authors present a modified problem with is non-negative and zero precisely at solutions and consider its quasiconvexification. This problem has a connection to a boundary condition for \(u_1\) and \(u_2\). Numerical tests investigate the functioning of Newton-Raphson method for solving the nonlinear system of equations.
reviewed by: Tommi Brander
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35G60
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N21
zbMATH DE Number: 7355288
zbMATH Keywords: Calderón's problem
zbMATH Keywords: Euler-Lagrange equation
zbMATH Keywords: quasiconvexification
zbMATH Keywords: Newton-Raphson method
describes a project that uses: FreeFem++
MaRDI profile type: Publication
full work available at URL: s00526-021-01945-3
OpenAlex ID: W3162201923
Wikidata QID: Q114229012
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DOI: 10.1007/S00526-021-01945-3
description: scientific article; zbMATH DE number 7355288