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Esteban, M. J.; Lions, Pierre-Louis

A compactness lemma. (English) Zbl 0512.46035

Nonlinear Anal., Theory Methods Appl. 7, 381-385 (1983).
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Cited in 26 Documents

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46A50 Compactness in topological linear spaces; angelic spaces, etc.

Keywords:

Sobolev spaces; compact imbedding; symmetry of domain; spaces of functions with spherical symmetry with respect to a group of variables; Sobolev exponent
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\textit{M. J. Esteban} and \textit{P.-L. Lions}, Nonlinear Anal., Theory Methods Appl. 7, 381--385 (1983; Zbl 0512.46035)
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References:

[1] Berestycki, H.; Lions, P.L., Existence of a ground state in nonlinear equations of the type Klein-Gordon, () · Zbl 0707.35143
[2] B{\scerestycki} H. & L{\scions} P.L., Nonlinear scalar fields equations, Archs. ration Mech. Analysis, to appear.
[3] Brascamp, H.J.; Lieb, E.H.; Luttinger, J.M., A general rearrangement inequality for multiple integrals, J. funct. analysis, 17, 227-237, (1974) · Zbl 0286.26005
[4] Esteban, M.J., Nonlinear elliptic problems in strip-like domains: symmetry of positive vortex rings, Nonlinear analysis, 7, 365-379, (1983) · Zbl 0513.35035
[5] Lieb, E.H., Existence and uniqueness of the minimizing solutions of Choquard’s nonlinear equation, Stud. appl. math., 57, 93-105, (1977) · Zbl 0369.35022
[6] L{\scions} P.L., in preparation.
[7] Lions, P.L., Minimization problems in L1(\(R\)N), J. funct. analysis, 41, 236-275, (1981)
[8] Lions, P.L., Quelques remarques sur la symétrisation de Schwarz, Nonlinear partial differential equations and their applications. college de France seminar, Vol. I, (1981), Pitman London · Zbl 0467.35008
[9] Polya, G.; Szego, G., Isoperimetric inequalities in mathematical physics, (1951), Princeton University Press Princeton · Zbl 0044.38301
[10] Strauss, W., Existence of solitary waves in higher dimensions, Communs. math. physics, 55, 149-162, (1977) · Zbl 0356.35028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.