Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

Yong Hah Lee

doi:10.1007/s11118-013-9377-2

Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

Yong Hah Lee

Department of Mathematics Education

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

1 Scopus citations

Abstract

We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.

Original language	English
Pages (from-to)	463-468
Number of pages	6
Journal	Potential Analysis
Volume	41
Issue number	2
DOIs	https://doi.org/10.1007/s11118-013-9377-2
State	Published - Jun 2014

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012006926).

Keywords

Asymptotic boundary value problem
Harmonic boundary
Harmonic map

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10.1007/s11118-013-9377-2

Cite this

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title = "Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary",

abstract = "We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.",

keywords = "Asymptotic boundary value problem, Harmonic boundary, Harmonic map",

author = "Lee, {Yong Hah}",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012006926).",

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AB - We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.

KW - Asymptotic boundary value problem

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KW - Harmonic map

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DO - 10.1007/s11118-013-9377-2

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Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

Abstract

Bibliographical note

Keywords

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