Magneto-static vortices in two dimensional Abelian gauge theories
Abstract
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 φ=0. This result, due to the lack of suitable embedding theorems for the vector potential is achieved with the help of a penalization method.
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