Revista Matemática Iberoamericana


Full-Text PDF (302 KB) | Metadata | Table of Contents | RMI summary
Volume 20, Issue 1, 2004, pp. 33–66
DOI: 10.4171/RMI/379

Published online: 2004-04-30

Critical nonlinear elliptic equations with singularities and cylindrical symmetry

Marino Badiale[1] and Enrico Serra[2]

(1) Università degli Studi di Torino, Italy
(2) Politecnico di Torino, Italy

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.

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

Badiale Marino, Serra Enrico: Critical nonlinear elliptic equations with singularities and cylindrical symmetry. Rev. Mat. Iberoamericana 20 (2004), 33-66. doi: 10.4171/RMI/379