Magneto-static vortices in two-dimensional Abelian gauge theories. (English) Zbl 1181.35227

Summary: 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 \({\mathbf A}\) is achieved with the help of a penalization method.


35Q53 KdV equations (Korteweg-de Vries equations)
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
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