Minimisers of supremal functionals and mass-minimising 1-currents
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912542330191872 |
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| author | Katzourakis, Nikos Moser, Roger |
| author_facet | Katzourakis, Nikos Moser, Roger |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimisers of supremal functionals and mass-minimising 1-currents Katzourakis, Nikos Moser, Roger Analysis of PDEs 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. |
| title | Minimisers of supremal functionals and mass-minimising 1-currents |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.06727 |