Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 10
87
Views
4
CrossRef citations to date
0
Altmetric
Articles

On the maximizing problem associated with Sobolev-type embeddings under inhomogeneous constraints

&
Pages 1916-1934 | Received 30 Jan 2018, Accepted 19 Jun 2018, Published online: 17 Jul 2018

References

  • Lieb EH. The stability of matter. Rev Mod Phys. 1976;48:553–569. doi: 10.1103/RevModPhys.48.553
  • Moser J. A sharp form of an inequality by N. Trudinger. Indiana Univ Math J. 1970;20:1077–1092. doi: 10.1512/iumj.1971.20.20101
  • Pohozaev SI. The Sobolev embedding in the case pl=n. Proceedings of the Technical Scientific Conference on Advances of Scientific Research 1964–1965; Mathematics Section, Moscow: Moskov. Energetics Inst.; 1965. p. 158–170.
  • Trudinger NS. On imbeddings into Orlicz spaces and some applications. J Math Mech. 1967;17:473–483.
  • Yudovich VI. Some estimates connected with integral operators and with solutions of elliptic equations. Dok Akad Nauk SSSR. 1961;138:804–808.
  • Adachi S, Tanaka K. A scale-invariant form of Trudinger–Moser inequality and its best exponent. Proc Amer Math Soc. 1999;1102:148–153.
  • Cao DM. Nontrivial solution of semilinear elliptic equation with critical exponent in R2 . Comm Partial Differ Equ. 1992;17:407–435. doi: 10.1080/03605309208820848
  • Li Y, Ruf B. A sharp Trudinger–Moser type inequality for unbounded domains in Rn . Indiana Univ Math J. 2008;57:451–480. doi: 10.1512/iumj.2008.57.3137
  • Ruf B. A sharp Trudinger–Moser type inequality for unbounded domains in R2 . J Funct Anal. 2005;219:340–367. doi: 10.1016/j.jfa.2004.06.013
  • Ishiwata M, Wadade H. On the effect of equivalent constraints on a maximizing problem associated with the Sobolev type embeddings in RN . Math Ann. 2016;364:1043–1068. doi: 10.1007/s00208-015-1243-7
  • Ishiwata M. Existence and nonexistence of maximizers for variational problems associated with Trudinger–Moser type inequalities in RN . Math Ann. 2011;351:781–804. doi: 10.1007/s00208-010-0618-z
  • Lam N, Lu G, Zhang L. Equivalence of critical and subcritical sharp Trudinger–Moser–Adams inequalities. to appear in Rev. Mat. Iberoam. 2017;arXiv:1504.04858.
  • Do Ó JM, Sani F, Tarsi C. Vanishing-concentration-compactness alternative for the Trudinger-Moser inequality in RN . Commun Contemp Math. 2016;1650036:27 pages.
  • Carleson L, Chang SYA. On the existence of an extremal function for an inequality of J. Moser Bull Sci Math. 1986;110:113–127.
  • Flucher M. Extremal functions for the Trudinger-Moser inequality in 2 dimensions. Comm Math Helv. 1992;67:471–497. doi: 10.1007/BF02566514
  • Lam N, Lu G. Sharp singular Adams inequalities in high order Sobolev spaces. Methods Appl Anal. 2012;19:243–266.
  • Lin KC. Extremal functions for Moser's inequality. Trans Amer Math Soc. 1996;348:2663–2671. doi: 10.1090/S0002-9947-96-01541-3
  • Ruf B, Sani F. Sharp Adams-type inequalities in Rn . Trans Amer Math Soc. 2013;365:645–670. doi: 10.1090/S0002-9947-2012-05561-9
  • Nguyen VH. Maximizers for the variational problems associated with Sobolev type inequalities under constraints. arXiv:1705.08434.
  • Weinstein MI. Nonlinear Schrodinger equations and sharp interpolation estimates. Commun Math Phys. 1982/1983;87:567–576. doi: 10.1007/BF01208265

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.