A coercive James’s weak compactness theorem and nonlinear variational problems |
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Authors: | J Orihuela |
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Institution: | a Universidad de Murcia, Dpto. Matemáticas, 30.100 Espinardo, Murcia, Spainb Universidad de Granada, E.T.S. Ingeniería de Edificación, Dpto. Matemática Aplicada, c/ Severo Ochoa s/n, 18071, Granada, Spain |
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Abstract: | We discuss a perturbed version of James’s sup theorem for weak compactness that not only properly generalizes that classical statement, but also some recent extensions of this central result: the sublevel sets of an extended real valued and coercive function whose subdifferential is surjective are relatively weakly compact. Furthermore, we apply it to generalize and unify some facts in mathematical finance and to prove that the unique possible framework in the development of an existence theory for a wide class of nonlinear variational problems is the reflexive one. |
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Keywords: | 46B10 49J52 47J20 46N10 91B30 |
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