Abstract
We give a precise description of all G-invariant Palais-Smale sequences for the variational problem associated with an elliptic Dirichlet problem at critical growth on a bounded domain which is invariant under the action of a groupGof orthogonal transformations.
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References
Th. AubinProblèmes isopérimétriques et espaces de SobolevJ. Diff. Geom. 11 (1976), 573–598.
H. BrézisElliptic equations with limiting Sobolev exponents ¡ª The impact of topologyComm Pure Appl. Math. 39 (1986), S17¡ªS39.
Brézis, H. and Lieb, E.A relation between pointwise convergence of functions and convergence of functionalsProc. Amer. Math. Soc. 88 (1983), 486–490.
M. ClappOn the number of positive symmetric solutions of a nonautonomous semi-linear elliptic problemNonl. Anal. 42 (2000), 405–422.
M. Clapp, G. IzquierdoMultiple positive symmetric solutions of a singularly perturbed elliptic equationTopol. Meth. in Nonl. Anal., to appear.
M. Clapp, O. Kavian, and B. RufMultiple solutions of nonhomogeneous elliptic equations with critical nonlinearity on symmetric domainspreprint.
T. tom DieckTransformation groupsde Gruyter Studies in Math. 8, de Gruyter, Berlin-New York 1987
P.L. LionsSymmetries and the concentration compactness methodin Nonlinear variational problemsResearch Notes in Math. 127, Pitman, London 1985, 47–56
S. PohozaevEigenfunctions of the equationDu + Af (u) =0, Soviet Math. Dokl. 6 (1965), 1408–1411
M. StruweA global compactness result for elliptic boundary value problems involving limiting nonlinearities Math. Z. 187 (1984), 511–517
M. StruweVariational Methods. Applications to nonlinear partial differential equations and Hamiltonian systemsSpringer, Berlin-Heidelberg 1990.
G. TalentiBest constant in Sobolev inequalityAnn. Mat. Pura Appl. 110 (1976), 353–372
M. Willem Minimax theorems, PNLDE 24, Birkhäuser, Boston-Basel-Berlin 1996
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Clapp, M. (2003). A Global Compactness Result for Elliptic Problems with Critical Nonlinearity on Symmetric Domains. In: Lupo, D., Pagani, C.D., Ruf, B. (eds) Nonlinear Equations: Methods, Models and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8087-9_9
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DOI: https://doi.org/10.1007/978-3-0348-8087-9_9
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