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2007 Critical functions and elliptic PDE on compact Riemannian manifolds
Stephane Collion
Adv. Differential Equations 12(1): 55-120 (2007).

Abstract

We study in this work the existence of minimizing solutions to the critical-power type equation $\triangle _{\textbf{g}}u+h.u=f .u^{\frac{n+2}{n-2}} $ on a compact Riemannian manifold in the limit case normally not solved by variational methods. For this purpose, we use a concept of "critical function" that was originally introduced by E. Hebey and M. Vaugon for the study of the second best constant in the Sobolev embeddings. Along the way, we prove an important estimate concerning concentration phenomenas when $f$ is a non-constant function.

Citation

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Stephane Collion. "Critical functions and elliptic PDE on compact Riemannian manifolds." Adv. Differential Equations 12 (1) 55 - 120, 2007.

Information

Published: 2007
First available in Project Euclid: 18 December 2012

zbMATH: 1157.53334
MathSciNet: MR2272821

Subjects:
Primary: 58J05
Secondary: 35B33, 35J20, 35J60, 53C21

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.12 • No. 1 • 2007
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