L∞ Variational Problems with Running Costs and Constraints

Various approaches are used to derive the Aronsson–Euler equations for L∞ calculus of variations problems with constraints. The problems considered involve holonomic, nonholonomic, isoperimetric, and isosupremic constraints on the minimizer. In addition, we derive the Aronsson–Euler equation for the basic L∞ problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.