Invariance of flows in doubly-connected domains with the same modulus

Abstract

We consider systems of elliptic partial differential equations in divergence form with Dirichlet’s boundary conditions in doubly-connected domain of the plane with modulus \({\mu }\). We prove an invariance property of the corresponding global flows in the class of domains with the same modulus. Applications are given to the problem of electrical heating of a conductor whose thermal and electrical conductivities depend on the temperature and to the flow of a viscous fluid in a porous medium, taking into account the Soret and Dufour’s effects.