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Bubbles over Bubbles: A C0-theory for the Blow-up of Second Order Elliptic Equations of Critical Sobolev Growth

  • Emmanuel Hebey
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 59)

Abstract

Let (M, g,) be a smooth compact Riemannian manifold of dimension n ≥ 3, and △ g =-div g ▽ be the Laplace-Beltrami operator. Let also 2* be the critical Sobolev exponent for the embedding of the Sobolev space H 1 2 (M) into Lebesgue’s spaces, and h be a smooth function on M. Elliptic equations of critical Sobolev growth like
$$\Delta _g u + hu = u^{2^* - 1} $$
have been the target of investigation for decades. A very nice H 1 2 -theory for the asymptotic behaviour of solutions of such an equation is available since the 1980’s. We discuss here the C 0-theory recently developed by Druet, Hebey and Robert. Such a theory provides sharp pointwise estimates for the asymptotic behaviour of solutions of the above equation.

Keywords

Scalar Curvature Sobolev Inequality Limit Equation Order Elliptic Equation Minimal Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Emmanuel Hebey
    • 1
  1. 1.Département de Mathématiques Site de Saint-MartinUniversité de Cergy-PontoiseCergy-Pontoise cedexFrance

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