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Smooth variational principles with constraints

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Abstract.

We prove a smooth variational principle with constraints, when the set of constraints is a finite dimensional subspace. A counterexample shows that this result does not remain true if the set of constraints is infinite dimensional. We also obtain a counterexample to the fuzzy sum rule for the subdifferential of two lower semi continuous in infinite dimensional Banach spaces.

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Authors and Affiliations

  1. Laboratoire de Mathématiques pures, Université Bordeaux I, 351, cours de la Libération, F-33405 Talence Cedex, France, , , , , , FR

    Robert Deville

  2. Section of Mathematical Analysis, Department of Mathematics, Sofia University, 5 James Bourchier Blvd., BG-1126 Sofia, Bulgaria, , , , , , BG

    Milen Ivanov

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  1. Robert Deville
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  2. Milen Ivanov
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Received: 22.4.1996; final version received 14.1.1997.

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Deville, R., Ivanov, M. Smooth variational principles with constraints. Arch. Math. 69, 418–426 (1997). https://doi.org/10.1007/s000130050140

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  • DOI: https://doi.org/10.1007/s000130050140

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