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March, 2004 Critical nonlinear elliptic equations with singularities and cylindrical symmetry
Marino Badiale, Enrico Serra
Rev. Mat. Iberoamericana 20(1): 33-66 (March, 2004).

Abstract

Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in $\mathbb{R}^{N}$ with cylindrical symmetry and with singularities on a whole subspace of $\mathbb{R}^{N}$. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.

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Marino Badiale. Enrico Serra. "Critical nonlinear elliptic equations with singularities and cylindrical symmetry." Rev. Mat. Iberoamericana 20 (1) 33 - 66, March, 2004.

Information

Published: March, 2004
First available in Project Euclid: 2 April 2004

zbMATH: 1330.35137
MathSciNet: MR2076771

Subjects:
Primary: 35B33 , 35J20

Keywords: Critical exponents , cylindrical symmetry , loss of compactness , singularities

Rights: Copyright © 2004 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.20 • No. 1 • March, 2004
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