Partial regularity for mass-minimizing currents in Hilbert spaces

Ambrosio Luigi - De Lellis Camillo - Schmidt Thomas

year: 2015
journal: J. Reine Angew. Math.
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|],[37|]]] 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 [[[32|]]], 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.

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