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Blow-up solutions for linear perturbations of the Yamabe equation

Abstract : For a smooth, compact Riemannian manifold (M,g) of dimension $N \geg 3$, we are interested in the critical equation $$\Delta_g u+(N-2/4(N-1) S_g+\epsilon h)u=u^{N+2/N-2} in M, u>0 in M,$$ where \Delta_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,\alpha}(M)$, and $\epsilon$ is a small parameter.
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https://hal.archives-ouvertes.fr/hal-00769041
Contributor : Jérôme Vétois <>
Submitted on : Thursday, December 27, 2012 - 6:12:34 PM
Last modification on : Monday, October 12, 2020 - 10:27:31 AM

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  • HAL Id : hal-00769041, version 1
  • ARXIV : 1210.6165

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Pierpaolo Esposito, Angela Pistoia, Jérôme Vétois. Blow-up solutions for linear perturbations of the Yamabe equation. Concentration Analysis and Applications to PDE (ICTS Workshop, Bangalore, January 2012), Trends in Mathematics, Birkhäuser/Springer Basel, pp.29-47, 2013, Trends in Mathematics. ⟨hal-00769041⟩

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