On isosupremic vectorial minimisation problems in L^∞ with general nonlinear constraints

2022/02/24 by Ed Clark, Clark, Ed, Nikos Katzourakis +1
Computer Science · Mathematics · #Analytic and geometric function theory #Contact Mechanics and Variational Inequalities #Nonlinear Partial Differential Equations #math.AP #math.OC #msc:35J92 #msc:35J94 #msc:49J20 #msc:49K20 #msc:49K35 #msc:49K99

paper · pdf · doi:10.48550/arxiv.2202.12005

27 pages, 1 table

arxiv created 2022/02/24 · arxiv updated 2022/02/25

Abstract

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 L^p 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.

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