In this paper we prove the existence of a smooth minimum for the Yang–Mills–Higgs functional over a disk in 3 dimensions among those configurations with monopoles with prescribed degree, which are covariant constant at the boundary. These boundary conditions come essentially from a 4-dimensional generalized Neumann problem for the pure Yang–Mills functional and dimensional reduction. This problem is well-posed only as a gauge theory in dimension 3. It extends analogous results on Ginzburg–Landau vortices in 2 dimensions.
A Boundary Value Problem for Monopoles over a 3-dimensional Disk
MARINI, ANTONELLA
2004-01-01
Abstract
In this paper we prove the existence of a smooth minimum for the Yang–Mills–Higgs functional over a disk in 3 dimensions among those configurations with monopoles with prescribed degree, which are covariant constant at the boundary. These boundary conditions come essentially from a 4-dimensional generalized Neumann problem for the pure Yang–Mills functional and dimensional reduction. This problem is well-posed only as a gauge theory in dimension 3. It extends analogous results on Ginzburg–Landau vortices in 2 dimensions.File in questo prodotto:
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