Parametrized Measures and Variational Principles

Pedregal, Pablo

doi:10.1007/978-3-0348-8886-8

Cited by 350 publications

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“…A characterization of Young measures generated by gradients was completely given by Kinderlehrer and Pedregal [21,22], cf. also [32,33]. To our knowledge, the first attempt to characterize both oscillations and concentrations in sequences of gradients is due to Fonseca, Müller, and Pedregal [14].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Oscillations and concentrations in sequences of gradients

Kałamajska

Kružík

2007

ESAIM: COCV

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“…The Young measure theory has been developed in [3,8,10] following the original idea of Young [12]. The last conclusion concerning inequality (2.5) can be found in [8] and also follows from (2.4) using the biting convergence in L 1 (0, 1) (see also [1,4,7]). …”

Section: In This Case We Say the Subsequence {U K J } Converges To (mentioning

confidence: 98%

“…The proof of the sufficiency part (Theorem 3.3) of this theorem relies on the Young measure theory as developed in [3,8,10] following the original idea of Young [12].…”

Section: Introductionmentioning

confidence: 99%

(PS)-weak lower semicontinuity in one dimension: A necessary and sufficient condition

Vasiliu

Yan

2007

Nonlinear Analysis: Theory, Methods & Applications

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“…Moreover weak lower semicontinuity is equivalent to convexity of the functionals involved in those variables where we have weak but not strong convergence ( [13]). We treat those two issues succesively.…”

Section: Existence Of Optimal Solutionsmentioning

confidence: 99%

Optimal design of a plate of variable thickness: a variational approach in dimension one

Pedregal¹,

Donoso²

2003

Mat. apl. comput.

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Abstract. For a typical design problem of a plate of variable thickness, we analyze the onedimensional situation through a variational reformulation to discover that, in contrast with the higher dimensional case, there are optimal solutions. Another typical interpretation of this simplification is that of the optimal shape of a bending beam. The mechanism employed for the existence issue is the direct method for the new formulation. Optimality conditions are then pursued.Mathematical subject classification: 49J15, 49J45, 49K15, 74K20, 74P05.

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Parametrized Measures and Variational Principles

Cited by 350 publications

References 0 publications

Oscillations and concentrations in sequences of gradients

Oscillations and concentrations in sequences of gradients

(PS)-weak lower semicontinuity in one dimension: A necessary and sufficient condition

Optimal design of a plate of variable thickness: a variational approach in dimension one

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