TY - JOUR

T1 - Interior continuity of two-dimensional weakly stationary-harmonic multiple-valued functions

AU - Lin, Chun Chi

PY - 2014/7

Y1 - 2014/7

N2 - 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.

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.

KW - Almgren's big regularity paper

KW - Interior continuity

KW - Multiple-valued functions

KW - Weakly stationary-harmonic

UR - http://www.scopus.com/inward/record.url?scp=84904381482&partnerID=8YFLogxK

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U2 - 10.1007/s12220-012-9385-2

DO - 10.1007/s12220-012-9385-2

M3 - Article

AN - SCOPUS:84904381482

VL - 24

SP - 1547

EP - 1582

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 3

ER -