Homogeneous and isotropic statistical solutions of the Navier-Stokes equations.
Dostoglou, S., Fursikov, A.V., Kahl, J.D. (2006)
Mathematical Physics Electronic Journal [electronic only]
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Dostoglou, S., Fursikov, A.V., Kahl, J.D. (2006)
Mathematical Physics Electronic Journal [electronic only]
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Hüngerbuhler, Norbert (1997)
The New York Journal of Mathematics [electronic only]
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Androulakis, George, Dostoglou, Stamatis Dostoglou (2004)
Mathematical Physics Electronic Journal [electronic only]
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Mikhail A. Sychev (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Martin Kružík (1998)
Commentationes Mathematicae Universitatis Carolinae
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The purpose of this note is to discuss the relationship among Rosenthal's modulus of uniform integrability, Young measures and DiPerna-Majda measures. In particular, we give an explicit characterization of this modulus and state a criterion of the uniform integrability in terms of these measures. Further, we show applications to Fatou's lemma.
Gisella Croce, Catherine Lacour, Gérard Michaille (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We show how to capture the gradient concentration of the solutions of Dirichlet-type problems subjected to large sources of order concentrated on an -neighborhood of a hypersurface of the domain. To this end we define the gradient Young-concentration measures generated by sequences of finite energy and establish a very simple characterization of these measures.
Martin Kružík, Johannes Zimmer (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Rate-independent problems are considered, where the stored energy density is a function of the gradient. The stored energy density may not be quasiconvex and is assumed to grow linearly. Moreover, arbitrary behaviour at infinity is allowed. In particular, the stored energy density is not required to coincide at infinity with a positively 1-homogeneous function. The existence of a rate-independent process is shown in the so-called energetic formulation.
Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.