On the minimality of the p-harmonic map x/|x|: Bn → Sn-1

Min Chun Hong

doi:10.1007/s005260100082

On the minimality of the p-harmonic map x/|x|: Bⁿ → S^n-1

Min Chun Hong^*

^*Corresponding author for this work

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

22 Citations (Scopus)

Abstract

We prove that for any real number p with 1 < p ≤ n - 1, the map x/|x| : Bⁿ → S^n-1 is the unique minimizer of the p-energy functional ∫_Bn |∇u|^p dx among all maps in W^1,p(Bⁿ, S^n-1) with boundary value x on ∂Bⁿ.

Original language	English
Pages (from-to)	459-468
Number of pages	10
Journal	Calculus of Variations and Partial Differential Equations
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s005260100082
Publication status	Published - Dec 2001

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title = "On the minimality of the p-harmonic map x/|x|: Bn → Sn-1",

abstract = "We prove that for any real number p with 1 < p ≤ n - 1, the map x/|x| : Bn → Sn-1 is the unique minimizer of the p-energy functional ∫Bn |∇u|p dx among all maps in W1,p(Bn, Sn-1) with boundary value x on ∂Bn.",

author = "Hong, \{Min Chun\}",

year = "2001",

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N2 - We prove that for any real number p with 1 < p ≤ n - 1, the map x/|x| : Bn → Sn-1 is the unique minimizer of the p-energy functional ∫Bn |∇u|p dx among all maps in W1,p(Bn, Sn-1) with boundary value x on ∂Bn.

AB - We prove that for any real number p with 1 < p ≤ n - 1, the map x/|x| : Bn → Sn-1 is the unique minimizer of the p-energy functional ∫Bn |∇u|p dx among all maps in W1,p(Bn, Sn-1) with boundary value x on ∂Bn.

UR - https://www.scopus.com/pages/publications/0013203167

U2 - 10.1007/s005260100082

DO - 10.1007/s005260100082

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

On the minimality of the p-harmonic map x/|x|: Bⁿ → S^n-1

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