This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1). © 2015 Elsevier Inc. All rights reserved.

A direct approach to Plateau's problem in any codimension

De Philippis, Guido;
2016-01-01

Abstract

This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1). © 2015 Elsevier Inc. All rights reserved.
2016
288
Jan
59
80
https://arxiv.org/abs/1501.07109
De Philippis, Guido; De Rosa, A.; Ghiraldin, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/15975
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