On isosupremic vectorial minimisation problems in l∞ with general nonlinear constraints

Clark, E. and Katzourakis, N. (2023) On isosupremic vectorial minimisation problems in l∞ with general nonlinear constraints. Advances in Calculus of Variations. ISSN 1864-8266 doi: 10.1515/acv-2022-0068

Abstract/Summary

We study minimisation problems in L∞ for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Examples of admissible operators include those expressing pointwise, unilateral, integral isoperimetric, elliptic quasilinear differential, jacobian and null Lagrangian constraints. Via the method of Lp approximations as p → ∞, we illustrate the existence of a special L∞ minimiser which solves a divergence PDE system involving certain auxiliary measures as coefficients. This system can be seen as a divergence form counterpart of the Aronsson PDE system which is associated with the constrained L∞ variational problem.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/111282
Identification Number/DOI	10.1515/acv-2022-0068
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	De Gryuter
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