Displaying similar documents to “On the measures of DiPerna and Majda”

Evolutionary problems in non-reflexive spaces

Martin Kružík, Johannes Zimmer (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

DiPerna-Majda measures and uniform integrability

Martin Kružík (1998)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

Oscillations and concentrations in sequences of gradients

Martin Kružík, Agnieszka Kałamajska (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, { ∇ u k } , bounded in L p ( Ø ; ℝ m × n ) if p > 1 and Ω ⊂ ℝ n is a bounded domain with the extension property in W 1 , p . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of Ω are required and links with lower semicontinuity...