Opuscula Math. 40, no. 1 (2020), 151-163

Opuscula Mathematica

Concentration-compactness results for systems in the Heisenberg group

Patrizia Pucci
Letizia Temperini

Abstract. In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9 (2020), 895–922] on some variants of the concentration-compactness principle in bounded PS domains \(\Omega\) of the Heisenberg group \(\mathbb{H}^n\). The concentration-compactness principle is a basic tool for treating nonlinear problems with lack of compactness. The results proved here can be exploited when dealing with some kind of elliptic systems involving critical nonlinearities and Hardy terms.

Keywords: Heisenberg group, concentration-compactness, critical exponents, Hardy terms.

Mathematics Subject Classification: 22E30, 35B33, 35J50, 58E30, 35H05, 35A23.

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  • Patrizia Pucci (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-7242-8485
  • Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
  • Letizia Temperini
  • Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy
  • Communicated by P.A. Cojuhari.
  • Received: 2020-01-07.
  • Revised: 2020-01-27.
  • Accepted: 2020-01-27.
  • Published online: 2020-02-17.
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Cite this article as:
Patrizia Pucci, Letizia Temperini, Concentration-compactness results for systems in the Heisenberg group, Opuscula Math. 40, no. 1 (2020), 151-163, https://doi.org/10.7494/OpMath.2020.40.1.151

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