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Uniqueness criteria for the adjoint equation in state-constrained elliptic optimal control. (English) Zbl 1230.35041

Linear elliptic equations with regular Borel measures as inhomogeneity are considered. Such equations appear in state-constrained optimal control problems. It is known, by a counter example of J. Serrin [Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 18, 385–387 (1964; Zbl 0142.37601)], that in the presence of non-smooth data a standard weak formulation does not ensure uniqueness for such equations. That fact motivates the authors to investigate different notions of solutions for linear elliptic PDEs with measure valued right-hand sides that guarantee uniqueness.

MSC:

35J25 Boundary value problems for second-order elliptic equations
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
49K20 Optimality conditions for problems involving partial differential equations

Citations:

Zbl 0142.37601
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References:

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