On a non-linear system of PDEs with application to tumor identification

Abstract

In this work we present the analysis of a non-linear system of PDEs in relation with a solution of an inverse problem in conductivity with application in tumor detection. This non-linear system of PDEs corresponds with the Euler-Lagrange optimality systems associated to a non-convex vector variational problem. We study the (quasi-)convexification of the vector variational problem and present an strategy to solve the inverse problem numerically.