Displaying similar documents to “Space averages and homogeneous fluid flows.”

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 1 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.

Homogenization of periodic nonconvex integral functionals in terms of Young measures

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 Γ -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.

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.

Boundary regularity of flows under perfect slip boundary conditions

Petr Kaplický, Jakub Tichý (2013)

Open Mathematics

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We investigate boundary regularity of solutions of generalized Stokes equations. The problem is complemented with perfect slip boundary conditions and we assume that the nonlinear elliptic operator satisfies non-standard ϕ-growth conditions. We show the existence of second derivatives of velocity and their optimal regularity.

Regularity results for a class of obstacle problems

Michela Eleuteri (2007)

Applications of Mathematics

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We prove some optimal regularity results for minimizers of the integral functional ∫ f ( x , u , D u ) d x belonging to the class K : = { u ∈ W 1 , p ( Ω ) u ≥ ψ } , where ψ is a fixed function, under standard growth conditions of p -type, i.e. L - 1 | z | p ≤ f ( x , s , z ) ≤ L ( 1 + | z | p ) .