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

Ambrosio L, Schmidt T (2013)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2013

Journal

Proceedings of the London Mathematical Society London Mathematical Society

Publisher: London Mathematical Society

Book Volume: 106

Pages Range: 1121-1142

Journal Issue: 5

URI: http://cvgmt.sns.it/paper/1762/

DOI: 10.1112/plms/pds066

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 w*-topology. © 2012 London Mathematical Society.

Authors with CRIS profile

Thomas Schmidt Department Mathematik

Involved external institutions

Scuola Normale Superiore di Pisa (SNS) IT Italy (IT)

How to cite

APA:

Ambrosio, L., & Schmidt, T. (2013). Compactness results for normal currents and the Plateau problem in dual Banach spaces. Proceedings of the London Mathematical Society, 106(5), 1121-1142. https://doi.org/10.1112/plms/pds066

MLA:

Ambrosio, Luigi, and Thomas Schmidt. "Compactness results for normal currents and the Plateau problem in dual Banach spaces." Proceedings of the London Mathematical Society 106.5 (2013): 1121-1142.

BibTeX: Download