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Research Article

On the maximizing problem associated with critical Sobolev inequality under inhomogeneous constraints

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Pages 681-700 | Received 04 Mar 2020, Accepted 21 Apr 2021, Published online: 15 Jan 2023

References

  • Ishiwata M, Wadade H. On the effect of equivalent constrain on a maximizing problem associated with the Sobolev type embedding in RN. Math Ann. 2016;364:1043–1068.
  • Ishiwata M. On variational problems associated with Sobolev type inequalities and related topics. Nonlinear Phenomena in Mathematics and Economics. The 4th Riemann International School of Mathematics, September 14–18; Varese, Italia. 2015.
  • Ishiwata M, Wadade H. On the maximizing problem associated with Sobolev-type embeddings under inhomogeneous constraints. Appl Anal. 2019;98(10):1916–1934.
  • Nguyen VH. Maximizers for the variational problems associated with Sobolev type inequalities under constraints. Math Ann. 2018;372(1–2):229–255.
  • Aubin T. Problèmes isopérimétriques et espaces de Sobolev. J Differential Geom. 1976;11:573–598.
  • Talenti G. Best constant in Sobolev inequality. Ann Mat Pura Appl. 1976;110:353–372.
  • Yudovič VI. Some estimates connected with integral operators and with solutions of elliptic equations (Russian). Dokl Akad Nauk SSSR. 1961;138:805–808.
  • Pohožaev SI. On the eigenfunctions of the equation Δu+λf(u)=0 (Russian). Dokl Akad Nauk SSSR. 1965;165:36–39.
  • Trudinger NS. On imbedding into Orlicz spaces and some applications. J Math Mech. 1967;17:473–483.
  • Moser J. A sharp form of an inequality by N. Trudinger. Indiana Univ Math J. 1970/71;20:1077–1092.
  • Adachi S, Tanaka K. Trudinger type inequalities in RN and their best constant. Proc Am Math Soc. 2000;128:2051–2057.
  • Cao DM. Nontrivial solution of semilinear elliptic equations with critical exponent in R2. Commun Partial Differ Equ. 1992;17:407–435.
  • Ruf B. A sharp Trudinger-Moser type inequality for unbounded domains in R2. J Funct Anal. 2005;219:340–367.
  • Li Y, Ruf B. A sharp Trudinger-Moser type inequality for unbounded domains in Rn. Indiana Univ Math J. 2008;57:451–480.
  • Ishiwara M. Existence and nonexistence of maximizers for variational problems associated with Trudinger–Moser inequalities in RN. Math Ann. 2011;351:781–804.
  • do Ó JM, Sani F, Tarsi C. Vanishing–concentration–compactness alternative for the Trudinger–Moser inequality in RN. Commun Contemp Math. 2018;20(1):1650036, 27pp.
  • Ikoma N, Ishiwata M, Wadade H. Existence and non-existence of maximizers for the Moser–Trudinger type inequalities under inhomogeneous constraints. Math Ann. 2019;373(1–2):831–851.
  • Lam N, Lu G, Zhang L. Equivalence of critical and subcritical sharp Trudinger–Moser–Adams inequalities. Rev Mat Iberoam. 2017;33(4):1219–1246.
  • Nguyen VH. The thresholds of the existence of maximizers for the critical sharp Moser–Trudinger inequality under constraints. Math Ann. 2021;380(3–4):1933–1958.

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