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Partial regularity for mass-minimizing currents in Hilbert spaces.
- Source :
- Journal für die Reine und Angewandte Mathematik; Jan2018, Vol. 2017 Issue 734, p99-144, 46p
- Publication Year :
- 2018
-
Abstract
- Recently, the theory of currents and the existence theory for Plateau's problem have been extended to the case of finite-dimensional currents in infinite-dimensional manifolds or even metric spaces; see [5] (and also [7, 39] for the most recent developments). In this paper, in the case when the ambient space is Hilbert, we provide the first partial regularity result, in a dense open set of the support, for n-dimensional integral currents which locally minimize the mass. Our proof follows with minor variants [34], implementing Lipschitz approximation and harmonic approximation without indirect arguments and with estimates which depend only on the dimension n and not on codimension or dimension of the target space. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2017
- Issue :
- 734
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 127788773
- Full Text :
- https://doi.org/10.1515/ crelle-2015-0011