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

Ambrosio Luigi - Schmidt Thomas

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

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