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Minimizing sequences in class-qualified deposit problems. (English) Zbl 1134.49015

Summary: We study multidimensional control problems involving first-order partial differential equations. To ensure the existence of sufficiently regular multipliers (from the space \(C^*\) the first-order necessary optimality conditions, some restrictions of the feasible domain have to be added. In particular, we investigate ‘class-qualified’ problems where the weak derivatives of \(x\) can be represented within a Baire function class. In the present paper, we prove conditions under which the original and the modified problems possess the same minimal values.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
26B35 Special properties of functions of several variables, Hölder conditions, etc.
26E25 Set-valued functions
49Q20 Variational problems in a geometric measure-theoretic setting
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