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Erschienen in:
Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures

verfasst von : Agnieszka Kałamajska, Stefan Krömer, Martin Kružík

Erschienen in: Trends in Applications of Mathematics to Mechanics

Verlag: Springer International Publishing

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Abstract

It is well known that besides oscillations, sequences bounded only in L 1 can also develop concentrations, and if the latter occurs, we can at most hope for weak∗ convergence in the sense of measures. Here we derive a new tool to handle mutual interferences of an oscillating and concentrating sequence with another weakly converging sequence. We introduce a couple of explicit examples showing a variety of possible kinds of behavior and outline some applications in Sobolev spaces.

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Vorheriges Kapitel Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints
Nächstes Kapitel What Does Rank-One Convexity Have to Do with Viscosity Solutions?
Fußnoten
1
In [16] it is assumed that the compactification of the entire space \({\mathbb R}^m\times {\mathbb R}^{m\times n}\) is a subset in \({\mathbb R}^N\) for some \(N\in {\mathbb N}\). This however is not required for the proof in [16] which only uses separability of the compactification.
 
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Metadaten
Titel
Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures
verfasst von
Agnieszka Kałamajska
Stefan Krömer
Martin Kružík
Copyright-Jahr
2018
Buch
Trends in Applications of Mathematics to Mechanics

Print ISBN: 978-3-319-75939-5

Electronic ISBN: 978-3-319-75940-1

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-75940-1_2