Year: 2024
Type: article
Abstract: We study vector-valued functions that minimise the $$L^\infty $$ 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 (Commun Partial Differ Equ 30:1401–1428, 2005). We therefore obtain an extension of their theory.
Authors: Nikos Katzourakis, Roger Moser
Institutions: University of Reading, University of Bath
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4405055559