Abstract

A slice distance for the class of weak abelian L-P-bundles in 3 dimensions was introduced in [20], where it was used to prove the closure of such class of bundles for the weak L-P-convergence. We further investigate this distance here, and we prove more properties of it, for example we show that it is Holder-continuous on the slices of an L-P-bundle. Using the same distance, we give a notion of a boundary trace, which allows to use the direct method for minimization problems on weak bundles with fixed trace. We then state some conjectures and some open questions. (C) 2014 Elsevier Inc. All rights reserved.