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Weak Lower Semicontinuity by Means of Anisotropic Parametrized Measures

  • Agnieszka Kałamajska
  • Stefan Krömer
  • Martin KružíkEmail author
Chapter
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Part of the Springer INdAM Series book series (SINDAMS, volume 27)

Abstract

It is well known that besides oscillations, sequences bounded only in L1 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.

Notes

Acknowledgements

This work was partly done during MK’s visiting Giovanni-Prodi professorship at the University of Würzburg, Germany. The hospitality and support of the Institute of Mathematics is gratefully acknowledged. This work was also supported by GAČR through projects 16-34894L and 17-04301S. The work of AK was supported by NCN grant 2011/03/N/ST1/00111.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Agnieszka Kałamajska
    • 1
  • Stefan Krömer
    • 2
  • Martin Kružík
    • 2
    Email author
  1. 1.Institute of MathematicsUniversity of WarsawWarsawPoland
  2. 2.The Czech Academy of Sciences, Institute of Information Theory and AutomationPraha 8Czech Republic

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