Notes on a slice distance for singular LpLp-bundles

A slice distance for the class of weak abelian LpLp-bundles in 3 dimensions was introduced in [20], where it was used to prove the closure of such class of bundles for the weak LpLp-convergence. We further investigate this distance here, and we prove more properties of it, for example we show that it is Hölder-continuous on the slices of an LpLp-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.