About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 908216, 4 pages
http://dx.doi.org/10.1155/2014/908216
Research Article

Trudinger-Moser Embedding on the Hyperbolic Space

Department of Mathematics, Renmin University of China, Beijing 100872, China

Received 6 November 2013; Accepted 26 December 2013; Published 18 February 2014

Academic Editor: Julio Rossi

Copyright © 2014 Yunyan Yang and Xiaobao Zhu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Moser, “A sharp form of an inequality by N. Trudinger,” Indiana University Mathematics Journal, vol. 20, pp. 1077–1091, 1971.
  2. S. Pohozaev, “The Sobolev embedding in the special case pl=n,” in Proceedings of the Technical Scientific Conference on Advances of Scientific Reseach 1964-1965, Mathematics Sections, pp. 158–170, Moscow Energetic Institute, 1965.
  3. N. S. Trudinger, “On embeddings into Orlicz spaces and some applications,” Journal of Applied Mathematics and Mechanics, vol. 17, pp. 473–484, 1967.
  4. D. Cao, “Nontrivial solution of semilinear elliptic equations with critical exponent in 2,” Communications in Partial Differential Equations, vol. 17, pp. 407–435, 1992.
  5. R. Panda, “Nontrivial solution of a quasilinear elliptic equation with critical growth in n,” Proceedings of the Indian Academy of Science, vol. 105, pp. 425–444, 1995.
  6. J. M. do Ó, “N-Laplacian equations in N with critical growth,” Abstract and Applied Analysis, vol. 2, pp. 301–315, 1997.
  7. B. Ruf, “A sharp Trudinger-Moser type inequality for unbounded domains in 2,” Journal of Functional Analysis, vol. 219, no. 2, pp. 340–367, 2005. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. Li and B. Ruf, “A sharp Trudinger-Moser type inequality for unbounded domains in N,” Indiana University Mathematics Journal, vol. 57, no. 1, pp. 451–480, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Adimurthi and Y. Yang, “An interpolation of hardy inequality and trudinger-moser inequality in N and its applications,” International Mathematics Research Notices, vol. 13, pp. 2394–2426, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. T. Aubin, “Sur la function exponentielle,” Comptes Rendus de l'Académie des Sciences. Series A, vol. 270, pp. A1514–A1516, 1970.
  11. P. Cherrier, “Une inegalite de Sobolev sur les varietes Riemanniennes,” Bulletin des Sciences Mathématiques, vol. 103, pp. 353–374, 1979.
  12. P. Cherrier, “Cas d'exception du theor`eme d'inclusion de Sobolev sur les varietes Riemanniennes et applications,” Bulletin des Sciences Mathématiques, vol. 105, pp. 235–288, 1981.
  13. L. Fontana, “Sharp borderline Sobolev inequalities on compact Riemannian manifolds,” Commentarii Mathematici Helvetici, vol. 68, no. 1, pp. 415–454, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. Y. Yang, “Trudinger-Moser inequalities on complete noncompact Riemannian manifolds,” Journal of Functional Analysis, vol. 263, pp. 1894–1938, 2012.
  15. Y. Yang, “Trudinger-Moser inequalities on the entire Heisenberg group,” Mathematische Nachrichten, 2013. View at Publisher · View at Google Scholar
  16. Y. Yang and X. Zhu, “A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space,” The Journal of Partial Differential Equations, vol. 26, no. 4, pp. 300–304, 2013.
  17. A. Adimurthi and K. Tintarev, “On a version of Trudinger-Moser inequality with Möbius shift invariance,” Calculus of Variations and Partial Differential Equations, vol. 39, no. 1-2, pp. 203–212, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. G. Mancini and K. Sandeep, “Moser-Trudinger inequality on conformal discs,” Communications in Contemporary Mathematics, vol. 12, no. 6, pp. 1055–1068, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Mancini, K. Sandeep, and C. Tintarev, “Trudinger-Moser inequality in the hyperbolic space N,” Advances in Nonlinear Analysis, vol. 2, no. 3, pp. 309–324, 2013.
  20. I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
  21. E. Hebey, Sobolev Spaces on Riemannian Maifolds, vol. 1635 of Lecture Notes in Mathematics, Springer, 1996.