Affiliation:
1. Department of Mathematics and Statistics , University of Reading , Whiteknights Campus, Pepper Lane , Reading RG6 6AX , United Kingdom
Abstract
Abstract
We study minimisation problems in
L
∞
{L^{\infty}}
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
{L^{p}}
approximations as
p
→
∞
{p\to\infty}
, we illustrate the existence of a special
L
∞
{L^{\infty}}
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
∞
{L^{\infty}}
variational problem.
Funder
Engineering and Physical Sciences Research Council
Subject
Applied Mathematics,Analysis