Displaying similar documents to “A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies”

Evolutionary problems in non-reflexive spaces

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.

Nonconcentrating generalized Young functionals

Tomáš Roubíček (1997)

Commentationes Mathematicae Universitatis Carolinae

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The Young measures, used widely for relaxation of various optimization problems, can be naturally understood as certain functionals on suitable space of integrands, which allows readily various generalizations. The paper is focused on such functionals which can be attained by sequences whose “energy” (= p th power) does not concentrate in the sense that it is relatively weakly compact in L 1 ( Ω ) . Straightforward applications to coercive optimization problems are briefly outlined.