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

created by schmidt on 20 Feb 2012
modified on 18 May 2013

[BibTeX]

Published Paper

Inserted: 20 feb 2012
Last Updated: 18 may 2013

Journal: Proc. Lond. Math. Soc. (3)
Volume: 106
Number: 5
Pages: 1121-1142
Year: 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 ${\rm w}^\ast$-topology