Functional Equations

Warga, J.

doi:10.1016/b978-0-12-735150-6.50007-5

Cited by 37 publications

(48 citation statements)

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“…A classical result [39,42] is that, for every sequence {y k } k∈N bounded in L ∞ (Ω; R m×n ), there exists its subsequence (denoted by the same indices for notational simplicity) and a Young…”

Section: Young Measuresmentioning

confidence: 99%

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Oscillations and concentrations in sequences of gradients

Kałamajska

Kružík

2007

ESAIM: COCV

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Abstract.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 (Ω; 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 results by Meyers and by Acerbi and Fusco are also discussed.Mathematics Subject Classification. 49J45, 35B05.

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Section: Young Measuresmentioning

confidence: 99%

“…x ∈Ω the collection {ν x } x∈Ω is the so-called Young measure on (Ω, σ) ( [43], see also [5,36,39,41,42]). …”

Section: Definition and Basic Propertiesmentioning

confidence: 99%

Oscillations and concentrations in sequences of gradients

Kałamajska

Kružík

2007

ESAIM: COCV

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“…We need some properties of set valued maps Γ defined on a metric space A with nonvoid value sets in a metric space X; compare, e.g., Castaing and Valadier [5], Aubin and Frankowska [2], or Warga [29].…”

Section: Chain Recurrence For Families Of Dynamical Systemsmentioning

confidence: 99%

Morse Decomposition, Attractors and Chain Recurrence

Ayala

Corbin

Conville

et al. 2006

Proyecciones (Antofagasta)

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The global behavior of a dynamical system can be described by its Morse decompositions or its attractor and repeller configurations. There is a close relation between these two approaches and also with (maximal) chain recurrent sets that describe the system behavior on finest Morse sets. These sets depend upper semicontinuously on parameters. The connection with ergodic theory is provided through the construction of invariant measures based on chains.

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“…For finite-dimensional control systems, relaxed controls have been systematically studied. We refer the reader to the books of Gamkrelidze [8], Berkovitz [3] and Warga [20] for details. For infinite-dimensional systems, most results are concerned with linear or semilinear evolution systems.…”

Section: Introductionmentioning

confidence: 99%