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Optimal boundary regularity of proper harmonic maps between asymptotically hyperbolic spaces

Part of: Representations of solutions Variational problems in infinite-dimensional spaces Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  11 September 2025

Jingru Niu
Jingru Niu*
Affiliation:
School of Mathematical Sciences, https://ror.org/022k4wk35 Beijing Normal University , Beijing 100875, The People’s Republic of China
*
e-mail: 202331130026@mail.bnu.edu.cn
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Abstract

This article studies the optimal boundary regularity of harmonic maps between a class of asymptotically hyperbolic spaces. To be precise, given any smooth boundary map with nowhere vanishing energy density, this article provides an asymptotic expansion formula for harmonic maps under the assumption of $C^1$ up to the boundary.

Keywords

Harmonic mapsboundary regularityasymptotically hyperbolic spaces

MSC classification

Primary: 35J57: Boundary value problems for second-order elliptic systems 35J60: Nonlinear elliptic equations 35C20: Asymptotic expansions 35B65: Smoothness and regularity of solutions 58E20: Harmonic maps , etc.

Information

Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 38
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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