Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 6 (2016), 1285-1315.

A complete study of the lack of compactness and existence results of a fractional Nirenberg equation via a flatness hypothesis, I

Wael Abdelhedi, Hichem Chtioui, and Hichem Hajaiej

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We consider a nonlinear critical problem involving the fractional Laplacian operator arising in conformal geometry, namely the prescribed σ-curvature problem on the standard n-sphere, n 2. Under the assumption that the prescribed function is flat near its critical points, we give precise estimates on the losses of the compactness and we provide existence results. In this first part, we will focus on the case 1 < β n 2σ, which is not covered by the method of Jin, Li, and Xiong (2014, 2015).

Article information

Anal. PDE, Volume 9, Number 6 (2016), 1285-1315.

Received: 17 March 2015
Revised: 26 November 2015
Accepted: 12 April 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35B33: Critical exponents 35B99: None of the above, but in this section 35R11: Fractional partial differential equations 58E30: Variational principles

fractional Laplacian critical exponent $\sigma$-curvature critical points at infinity


Abdelhedi, Wael; Chtioui, Hichem; Hajaiej, Hichem. A complete study of the lack of compactness and existence results of a fractional Nirenberg equation via a flatness hypothesis, I. Anal. PDE 9 (2016), no. 6, 1285--1315. doi:10.2140/apde.2016.9.1285.

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