Abstract
This article is devoted to the study of a non-well-set problem of optimal control for a system governed by an elliptic partial differential equation. By generalizing some classical methods in convex optimization, we state and prove the system of necessary and sufficient conditions for such a problem.
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References
Adams R (1975) Sobolev Spaces. Academic Press, New York
Berger M, Gauduchon P, Mazet E (1971) Spectre d'une Variété Riemannienne. Springer-Verlag, Berlin
Bourbaki N (1965) Integration, 2nd edn. Hermann, Paris
Demengel F, Temam R (1984) Convex functions of a measure and applications. Indiana Univ Math J 33:673–711
Demengel F, Temam R (to appear) Convex function of a measure and applications: the unbounded case, Actes des Journées Fermat, Toulouse
Dieudonne J (1971) Eléments d'Analyse, vol 4. Gauthier Villars, Paris
Ekeland I, Temam R (1972) Analyse Convexe et Problèmes Variationnels. Dunod, Paris
Geymonat G, Grisvard P (1964) Problèmes aux limites elliptiques dansL α. Cours de 3ème cycle, Université d'Orsay
Karcher H (1977) Riemannian center of mass and mollifier smoothing. Comm Pure Appl Math 30:509–543
Kohn R, Temam R (1983) Dual spaces of stresses and strains. Appl Math Optim 10:1–37
Lions JL (1973) Perturbations Singulières dans les Problèmes aux Limites et en Contróle Optimal. Springer-Verlag, Berlin
Lions JL (1981) Some Methods in the Mathematical Analysis of Systems and Their Control. Gordon and Breach, New York
Lions JL (1982) Problèmes aux Limites dans les Équations aux Dérivées Partielles. Presses de l'Université de Montréal, Montréal
Lions JL, Magenes E (1968) Problèmes aux limites Non Homogènes et Applications, vol 1. Dunod, Paris
McKean HP, Singer IM (1967) Curvature and the eigenvalues of the Laplacian. J Differential Geometry 1:43–69
Minakshisundaran S (1963) Eigenfunctions on Riemannian manifolds. J Indian Math Soc 17:159–165
Miranda C (1963–1966) Sulle proprieta di regolarita di certe transformazioni integrale. Mem Acad Lincei 7:303–336
Miranda C (1970) Partial Differential Equations of Elliptic Type, 2nd edn. Springer-Verlag, New York
Schwartz L (1966) Théorie des Distributions. Hermann, Paris
Sobolev S (1961) Sur les Équations aux Dérivées Partielles Hyperboliques Nonlinéaires. Edizioni Cremonese, Rome
Temam R (1983) Problèmes Mathématiques en Plasticité. Gauthier Villars, Paris
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Abergel, F. A non-well-posed problem in convex optimal control. Appl Math Optim 17, 133–175 (1988). https://doi.org/10.1007/BF01448364
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DOI: https://doi.org/10.1007/BF01448364