Existence Results for Minimizers of Parametric Elliptic Functionals

Guido De Philippis; Antonio De Rosa; Francesco Ghiraldin

doi:10.1007/s12220-019-00165-8

Existence Results for Minimizers of Parametric Elliptic Functionals

Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.

Original language	English (US)
Pages (from-to)	1450-1465
Number of pages	16
Journal	Journal of Geometric Analysis
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s12220-019-00165-8
State	Published - Apr 1 2020

Keywords

Elliptic integrand
Plateau problem
Wand varifolds

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-019-00165-8

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abstract = "We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.",

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AU - De Rosa, Antonio

AU - Ghiraldin, Francesco

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Y1 - 2020/4/1

N2 - We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.

AB - We prove a compactness principle for the anisotropic formulation of the Plateau problem in any codimension, in the same spirit of the previous works of the authors. In particular, we perform a new strategy for the proof of the rectifiability of the minimal set, based on the new anisotropic counterpart of the Allard rectifiability theorem proved in De Philippis et al. (Commun Pure Appl Math 71(6):1123–1148, 2016). As a consequence we provide a new proof of the Reifenberg existence theorem.

KW - Elliptic integrand

KW - Plateau problem

KW - Wand varifolds

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Existence Results for Minimizers of Parametric Elliptic Functionals

Abstract

Keywords

ASJC Scopus subject areas

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