Soluções de vórtice das equações de Ginzburg-Landau

Abstract

In this work we study a theorem of C.H. Taubes concerning vortex solution to the Ginzburg-Landau equations, which describe superconductivity. To prove the theorem we need to show the existence of a solution to a non-linear elliptic partial di erential equation of second order. To obtain the existence of solution we study a non-linear functional de ned on an appropriate Sobolev space. We also include two auxiliary chapters concerning complex line bundles and analytical preliminaries.