Weak closure of Singular Abelian $L^p$-bundles in $3$ dimensions

Mircea Petrache, Tristan Rivière

Published 2010-07-05, updated 2010-09-28Version 2

We prove the closure for the sequential weak $L^p$-topology of the class of vectorfields on $B^3$ having integer flux through almost every sphere. We show how this problem is connected to the study of the minimization problem for the Yang-Mills functional in dimension higher than critical, in the abelian case.