[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

A Compactness and Integral-Representation Result

  • Chapter
  • First Online:
A Variational Theory of Convolution-Type Functionals

Part of the book series: SpringerBriefs on PDEs and Data Science ((SBPDEDS))

  • 371 Accesses

Abstract

The main result of this chapter is a compactness and integral-representation result for the Γ-limits of the families {Fε(⋅, A)}ε, which we can obtain through a convolution version of the localization method of Γ-convergence. A key point is that it is possible to limit the analysis to finite-range convolutions through a truncation argument.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Braides, A.: Γ-Convergence for Beginners. Oxford Lecture Series in Mathematics and Its Applications, vol. 22. Oxford University Press, Oxford (2002)

    Google Scholar 

  2. Braides, A., Defranceschi, A.: Homogenization of Multiple Integrals. Oxford Lecture Series in Mathematics and Its Applications, vol. 12. The Clarendon Press/Oxford University Press, New York (1998)

    Google Scholar 

  3. Kreisbeck, C., Zappale, E.: Loss of double-integral character during relaxation. SIAM J. Math. Anal. 53, 351–385 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mora-Corral, C., Tellini, A.: Relaxation of a scalar nonlocal variational problem with a double-well potential. Calc. Var. Partial Differ. Equ. 59(67) (2020)

    Google Scholar 

  5. Pedregal, P.: Weak lower semicontinuity and relaxation for a class of non-local functionals. Rev. Mat. Complut. 29, 485–495 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Information Engineering, University of Cassino and Southern Lazio, Cassino, Frosinone, Italy

    Roberto Alicandro

  2. Department of Mathematics, Sapienza University of Rome, Rome, Italy

    Nadia Ansini

  3. SISSA, Trieste, Italy

    Andrea Braides

  4. Department of Technology, UiT The Arctic University of Norway, Narvik, Norway

    Andrey Piatnitski

  5. Institute for Applied Mathematics, University of Heidelberg, Heidelberg, Baden-Württemberg, Germany

    Antonio Tribuzio

Authors
  1. Roberto Alicandro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nadia Ansini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrea Braides
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrey Piatnitski
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Antonio Tribuzio
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Alicandro, R., Ansini, N., Braides, A., Piatnitski, A., Tribuzio, A. (2023). A Compactness and Integral-Representation Result. In: A Variational Theory of Convolution-Type Functionals. SpringerBriefs on PDEs and Data Science. Springer, Singapore. https://doi.org/10.1007/978-981-99-0685-7_5

Download citation

Publish with us

Policies and ethics

Search

Navigation