Interior continuity of two-dimensional weakly stationary-harmonic multiple-valued functions

研究成果: 雜誌貢獻文章

1 引文 (Scopus)

摘要

In his big regularity paper, Almgren has proven the regularity theorem for mass-minimizing integral currents. One key step in his paper is to derive the regularity of Dirichlet-minimizing QQ (ℝn)-valued functions in the Sobolev space γ2(Ω, QQ (ℝn)), where the domain Ω is open in ℝm . In this article, we introduce the class of weakly stationary-harmonic Q Q (ℝn)-valued functions. These functions are the critical points of Dirichlet's integral under smooth domain-variations and range-variations. We prove that if Ω is a two-dimensional domain in ℝ2 and f∈γ2 (Ω,QQ(ℝ n)) is weakly stationary-harmonic, then f is continuous in the interior of the domain Ω.

原文英語
頁(從 - 到)1547-1582
頁數36
期刊Journal of Geometric Analysis
24
發行號3
DOIs
出版狀態已發佈 - 2014 七月

指紋

Interior
Harmonic
Regularity
Dirichlet Integral
Sobolev Spaces
Dirichlet
Critical point
Theorem
Range of data

ASJC Scopus subject areas

  • Geometry and Topology

引用此文

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AB - In his big regularity paper, Almgren has proven the regularity theorem for mass-minimizing integral currents. One key step in his paper is to derive the regularity of Dirichlet-minimizing QQ (ℝn)-valued functions in the Sobolev space γ2(Ω, QQ (ℝn)), where the domain Ω is open in ℝm . In this article, we introduce the class of weakly stationary-harmonic Q Q (ℝn)-valued functions. These functions are the critical points of Dirichlet's integral under smooth domain-variations and range-variations. We prove that if Ω is a two-dimensional domain in ℝ2 and f∈γ2 (Ω,QQ(ℝ n)) is weakly stationary-harmonic, then f is continuous in the interior of the domain Ω.

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