Compactness results for normal currents and the Plateau problem in dual Banach spaces - Ambrosio, Luigi; Schmidt, Thomas (Proceedings of the London Mathematical Society, 2013)
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 w*-topology. © 2012 London Mathematical Society.
UnivIS-Import:2015-03-09:Pub.2013.nat.dma.lma2.compac