Title | Partial regularity for mass-minimizing currents in Hilbert spaces. |
Publication Type | Journal Article |
Year of Publication | 2018 |
Authors | Ambrosio L., De Lellis C., Schmidt T. |
Journal | Journal für die Reine und Angewandte Mathematik |
Volume | 2018 |
Pagination | 99–144 |
Date Published | June |
Publisher | De Gruyter |
Type of Article | Interior regularity |
ISSN | 0075-4102 |
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 [Acta Math. 185 (2000), 1?80] (and also [Proc. Lond. Math. Soc. (3) 106 (2013), 1121?1142], [Adv. Calc. Var. 7 (2014), 227?240] 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 [Indiana Univ. Math. J. 31 (1982), 415?434], 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. |
Notes | J. Reine Angew. Math. 734, 99-144 |
URL | https://www.degruyter.com/view/j/crelle.2018.2018.issue-734/issue-files/crelle.2018.2018.issue-734.xml |
DOI | 10.1515/crelle-2015-0011 |
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