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arXiv · 2403.06727

Minimisers of supremal functionals and mass-minimising 1-currents

Nikos Katzourakis·Roger Moser
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Abstract

We study vector-valued functions that minimise the $L^\infty$-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. We therefore obtain an extension of their theory.

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Nikos Katzourakis, Roger Moser. 2024-03-11. Minimisers of supremal functionals and mass-minimising 1-currents. https://doi.org/10.1007/s00526-024-02892-5

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