Calculus of Variations and Geometric Measure Theory
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M. Petrache - T. Rivière

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

created by petrache on 09 Jul 2010
modified on 07 Dec 2013


Published Paper

Inserted: 9 jul 2010
Last Updated: 7 dec 2013

Journal: Geometric and Functional Analysis
Volume: 21
Number: 6
Pages: 1419-1442
Year: 2011
Doi: 10.1007/s00039-011-0139-2


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.

Keywords: Topological singularities, Yang-Mills functional, weak L p -curvatures, singular bundles, weak compactness, closure theorem


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