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Transportation flow problems with Radon measure variables

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For a multidimensional control problem $(P)_K$ involving controls $u ∈ L_∞$, we construct a dual problem $(D)_K$ in which the variables ν to be paired with u are taken from the measure space rca (Ω,𝔅) instead of $(L_∞)*$. For this purpose, we add to $(P)_K$ a Baire class restriction for the representatives of the controls u. As main results, we prove a strong duality theorem and saddle-point conditions.
  • Cottbus University of Technology, Institute of Mathematics, Karl-Marx-Str. 17, P.O. Box 10 13 44, D-03013 Cottbus, Germany
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