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Compactness results for normal currents and the Plateau problem in dual Banach spaces
Author(s) -
Ambrosio Luigi,
Schmidt Thomas
Publication year - 2013
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pds066
Subject(s) - mathematics , dual polyhedron , eberlein–šmulian theorem , compact space , pure mathematics , banach space , banach manifold , dual (grammatical number) , class (philosophy) , uniformly convex space , fréchet space , boundary (topology) , interpolation space , mathematical analysis , lp space , functional analysis , art , literature , artificial intelligence , computer science , biochemistry , chemistry , gene
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.