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We study minimisation problems in $L^\infty$ for general quasiconvex firstorder functionals, where the class of admissible mappings is constrained by thesublevel sets of another supremal functional and by the zero set of a nonlinearoperator. Examples of admissible operators include those expressing pointwise,unilateral, integral isoperimetric, elliptic quasilinear differential, jacobianand null Lagrangian constraints. Via the method of $L^p$ approximations as$p\to \infty$, we illustrate the existence of a special $L^\infty$ minimiserwhich solves a divergence PDE system involving certain auxiliary measures ascoefficients. This system can be seen as a divergence form counterpart of theAronsson PDE system which is associated with the constrained $L^\infty$variational problem.

On isosupremic vectorial minimisation problems in $L^\infty$ with general nonlinear constraints