Minimisers of supremal functionals and mass-minimising 1-currents

Nikos Katzourakis; Roger Moser

doi:10.1007/s00526-024-02892-5

Minimisers of supremal functionals and mass-minimising 1-currents

Nikos Katzourakis, Roger Moser

Department of Mathematical Sciences

University of Reading

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

1 Citation (SciVal)

Abstract

We study vector-valued functions that minimise the L∞-norm of their derivatives for prescribed boundary data. We construct a vector-valued, mass minimising 1-current (i.e., a generalised geodesic) in the domain such that all solutions of the problem coincide on its support. Furthermore, this current can be interpreted as a streamline of the solutions. The construction relies on a p-harmonic approximation. In the case of scalar-valued functions, it is closely related to a construction of Evans and Yu (CommunPartialDifferEqu30:1401–1428, 2005). We therefore obtain an extension of their theory.

Original language	English
Article number	26
Journal	Calculus of Variations and Partial Differential Equations
Volume	64
Issue number	1
Early online date	6 Dec 2024
DOIs	https://doi.org/10.1007/s00526-024-02892-5
Publication status	Published - 31 Jan 2025

Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Acknowledgements

We wish to thank A. Backus for his comments on a previous version of this paper.

Funding

This work was partially supported by the Engineering and Physical Sciences Research Council (grant numbers EP/X017109/1 and EP/X017206/1).

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/X017109/1, EP/X017206/1
Engineering and Physical Sciences Research Council

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10.1007/s00526-024-02892-5Licence: CC BY

Cite this

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Minimisers of supremal functionals and mass-minimising 1-currents

Abstract

Data Availability Statement

Acknowledgements

Funding

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The Supreme Challenges of Supremal Functionals

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Minimisers of supremal functionals and mass-minimising 1-currents

Abstract

Data Availability Statement

Acknowledgements

Funding

Access to Document

Other files and links

Fingerprint

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The Supreme Challenges of Supremal Functionals

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