Critical nonlinear elliptic equations with singularities and cylindrical symmetry
Badiale, Marino ; Serra, Enrico
Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, p. 33-66 / Harvested from Project Euclid
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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.
Publié le : 2004-03-14
Classification:  critical exponents,  loss of compactness,  cylindrical symmetry,  singularities,  35J20,  35B33 
@article{1080928419,
     author = {Badiale, Marino and Serra, Enrico},
     title = {Critical nonlinear elliptic equations
with singularities and cylindrical symmetry},
     journal = {Rev. Mat. Iberoamericana},
     volume = {20},
     number = {1},
     year = {2004},
     pages = { 33-66},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1080928419}
}

Badiale, Marino; Serra, Enrico. Critical nonlinear elliptic equations
with singularities and cylindrical symmetry. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp.  33-66. http://gdmltest.u-ga.fr/item/1080928419/