## 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

#### Abstract

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

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

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

https://projecteuclid.org/euclid.apde/1510843323

Digital Object Identifier
doi:10.2140/apde.2016.9.1285

Mathematical Reviews number (MathSciNet)
MR3555312

Zentralblatt MATH identifier
1366.35211

#### Citation

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. https://projecteuclid.org/euclid.apde/1510843323

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