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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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Vol. 9 (2016), No. 6, 1285–1315
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Abstract |
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We consider a nonlinear critical problem involving the fractional Laplacian operator arising in conformal geometry, namely the prescribed -curvature problem on the standard -sphere, . 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 , which is not covered by the method of Jin, Li, and Xiong (2014, 2015). |
Keywords
fractional Laplacian, critical exponent,
$\sigma$-curvature, critical points at infinity
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Mathematical Subject Classification 2010
Primary: 35J60, 35B33, 35B99, 35R11, 58E30
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Milestones
Received: 17 March 2015
Revised: 26 November 2015
Accepted: 12 April 2016
Published: 3 October 2016
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Authors |
| Wael Abdelhedi | |
| Department of Mathematics Faculty of Sciences of Sfax 3018 Sfax Tunisia |
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| Hichem Chtioui | |
| Department of Mathematics Faculty of Sciences of Sfax 3018 Sfax Tunisia |
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| Hichem Hajaiej | |
| New York University Shanghai 1555 Century Avenue, Pudong 200122 Shanghai China |
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