Lipschitz measures and vector-valued Hardy spaces.

Folch-Gabayet, Magali; Guzmán-Partida, Martha; Pérez-Esteva, Salvador

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A refinement of Ball's theorem on Young measures.

Hüngerbuhler, Norbert (1997)

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DiPerna-Majda measures and uniform integrability

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.

The average length of a trajectory in a certain billiard in a flat two-torus.

Boca, F. P., Gologan, R. N., Zaharescu, A. (2003)

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A characterization of gradient Young-concentration measures generated by solutions of Dirichlet-type problems with large sources

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 $\frac{1}{\sqrt{ε}}$ concentrated on an $ε$ -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.