Magneto-static vortices in two dimensional Abelian gauge theories

Bellazzini, J.
Bonanno, C.
Siciliano, G.
Description
We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential $\phi=0$. This result, due to the lack of suitable embedding theorems for the vector potential $\A$ is achieved with the help of a penalization method.
Comment: 23 pages, no figures
Keywords
Mathematics - Analysis of PDEs, Mathematical Physics, 35J20, 35J60, 35Q60