Skip to main content
Log in

Concentration compactness of Moser functionals on manifolds

  • Original Paper
  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We will prove a concentration compactness property of the Moser functional on a compact Riemannian manifold.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Carleson L. and Chang S.Y.A. (1986). On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. 110(2): 113–127

    MATH  MathSciNet  Google Scholar 

  • do O’ J.M., Ruf B. and Figueiredo D.G. (2002). On an inequality by N. Trudinger and J. Moser and related elliptic equations. Comm. Pure. Appl. Math. 55: 135–152

    MATH  Google Scholar 

  • Fontana L. (1993). Sharp borderline Sobolev inequalities on compact Riemannian manifolds. Commun. Math. Helv. 68: 415–454

    Article  MATH  MathSciNet  Google Scholar 

  • Kichenassamy S. and Veron L. (1986). Singular solutions of the p-laplace equation. Math. Ann. 275: 599–615

    Article  MATH  MathSciNet  Google Scholar 

  • Lions P.L. (1985). The concentration-compactness principle in the calculus of variation, the limit case, Part I. Rev. Mat. Iberoamericana 1: 145–201

    MATH  MathSciNet  Google Scholar 

  • Li Y. (2001). Moser–Trudinger inequality on manifold of compact Riemannian of dimension two. J. Partial Differential Equations 14: 163–192

    MATH  MathSciNet  Google Scholar 

  • Li Y. (2005). Extremal functions for the Moser–Trudinger inequalities on compact Riemannian manifolds. Sci. China Ser. A 48: 618–648

    Article  MATH  MathSciNet  Google Scholar 

  • Li, Y.: Remarks on the extremal functions for the Moser–Trudinger inequalities. Acta Math. Sin. (to appear)

  • Lin K.C. (1996). Extremal functions for Moser’s inequality. Trans. Am. Math. Soc. 348: 2663–2671

    Article  MATH  Google Scholar 

  • Moser J. (1971). A sharp form of an inequality by N.Trudinger. Indiana Univ. Math. J. 20: 1077–1092

    Article  Google Scholar 

  • Serrin J. (1965). Isolated singularities of solutions of quasilinear equations. Acta Math. 113: 219–240

    Article  MATH  MathSciNet  Google Scholar 

  • Trudinger N.S. (1967). On embeddings into Orlicz space and some applications. J. Math. Mech. 17: 473–483

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuxiang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y. Concentration compactness of Moser functionals on manifolds. Ann Glob Anal Geom 32, 15–38 (2007). https://doi.org/10.1007/s10455-007-9062-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10455-007-9062-z

Keywords

Navigation