A characterization of convex calibrable sets in with respect to anisotropic norms
V. Caselles, A. Chambolle, S. Moll, M. Novaga (2008)
Annales de l'I.H.P. Analyse non linéaire
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V. Caselles, A. Chambolle, S. Moll, M. Novaga (2008)
Annales de l'I.H.P. Analyse non linéaire
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Philippe Bouafia (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
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We prove that there does not exist a uniformly continuous retraction from the space of continuous vector fields onto the subspace of vector fields whose divergence vanishes in the distributional sense. We then generalise this result using the concept of -charges, introduced by De Pauw, Moonens, and Pfeffer: on any subset satisfying a mild geometric condition, there is no uniformly continuous representation operator for -charges in .
Filippo Cammaroto, Paolo Cubiotti (1999)
Commentationes Mathematicae Universitatis Carolinae
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We deal with the integral equation , with , and . We prove an existence theorem for solutions where the function is not assumed to be continuous, extending a result previously obtained for the case .
Giuseppe Da Prato, Alessandra Lunardi (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study the realization of the operator in , where is a possibly unbounded convex open set in , is a convex unbounded function such that and , is the element with minimal norm in the subdifferential of at , and is a probability measure, infinitesimally invariant for . We show that , with domain is a dissipative self-adjoint operator in . Note that the functions in the domain of do not satisfy any particular boundary condition. Log-Sobolev and Poincaré inequalities...