L ∞ variational problems with running costs and constraints

摘要

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.