A1 Journal article (refereed)
Analytic characterization of monotone Hopf-harmonics (2022)

Kangasniemi, I., Koski, A., & Onninen, J. (2022). Analytic characterization of monotone Hopf-harmonics. Calculus of Variations and Partial Differential Equations, 61(4), Article 140. https://doi.org/10.1007/s00526-022-02246-z

JYU authors or editors

Publication details

All authors or editors: Kangasniemi, Ilmari; Koski, Aleksis; Onninen, Jani

Journal or series: Calculus of Variations and Partial Differential Equations

ISSN: 0944-2669

eISSN: 1432-0835

Publication year: 2022

Publication date: 20/05/2022

Volume: 61

Issue number: 4

Article number: 140

Publisher: Springer Science and Business Media LLC

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s00526-022-02246-z

Publication open access: Not open

Publication channel open access:

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2108.00258

Abstract

We study solutions of the inner-variational equation associated with the Dirichlet energy in the plane, given homeomorphic Sobolev boundary data. We prove that such a solution is monotone if and only if its Jacobian determinant does not change sign. These solutions, called monotone Hopf-harmonics, are a natural alternative to harmonic homeomorphisms. Examining the topological behavior of a solution (not a priori monotone) on the trajectories of Hopf quadratic differentials plays a sizable role in our arguments.

Keywords: partial differential equations; potential theory; functional analysis

Free keywords: 31C45; 35J25; 58E20; 74B20; 46E35; Hopf-Laplace equation; holomorphic quadratic differentials; inner-variational equations; monotone mappings, orientation-preserving Sobolev mappings; the principle of non-interpenetration of matter

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 2