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A compactness lemma. (English) Zbl 0512.46035


MSC:

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