# Compactness results for normal currents and the Plateau problem in dual Banach spaces

**published**
**year:** 2013

**journal:** Proc. Lond. Math. Soc. (3)

**abstract:** We consider the Plateau problem and the corresponding free boundary problem for finite-dimensional surfaces in possibly infinite-dimensional Banach spaces. For a large class of duals and in particular for reflexive spaces we establish the general solvability of these problems in terms of currents. As an auxiliary result we prove a new compactness theorem for currents in dual spaces, which in turn relies on a fine analysis of the ${\rm w}^\ast$-topology

The paper is available on the
cvgmt preprint server.