\(L ^{\infty }\) variational problems with running costs and constraints. (English) Zbl 1242.49049
Summary: Various approaches are used to derive the Aronsson-Euler equations for \(L ^{\infty }\) 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 \(L ^{\infty }\) problem with a running cost and then consider properties of an absolute minimizer. Many open problems are introduced for further study.
MSC:
| 49K21 | Optimality conditions for problems involving relations other than differential equations |
Keywords:
calculus of variations in \(L ^{\infty }\); constraints; running cost; Aronsson-Euler equationsReferences:
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