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Mathematische Annalen

, Volume 370, Issue 1–2, pp 287–308 | Cite as

The sharp affine \(L^2\) Sobolev trace inequality and variants

  • P. L. De Nápoli
  • J. Haddad
  • C. H. Jiménez
  • M. MontenegroEmail author
Article

Abstract

We establish a sharp affine \(L^p\) Sobolev trace inequality by using the \(L_p\) Busemann–Petty centroid inequality. For \(p = 2\), our affine version is stronger than the famous sharp \(L^2\) Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all extremizers in this case. For this new inequality, no Euclidean geometric structure is needed.

Mathematics Subject Classification

Primary 46E35 Secondary 46E39 51M16 

Notes

Acknowledgements

The authors are indebted to both referees for pointing out several references and several valuable comments on a previous version of this work.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • P. L. De Nápoli
    • 1
  • J. Haddad
    • 2
  • C. H. Jiménez
    • 3
  • M. Montenegro
    • 2
    Email author
  1. 1.IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires, Ciudad UniversitariaBuenos AiresArgentina
  2. 2.Departamento de Matemática, ICExUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  3. 3.Departamento de MatemáticaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil

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