Lions, Pierre-Louis Symétrie et compacité dans les espaces de Sobolev. (French) Zbl 0501.46032 J. Funct. Anal. 49, 315-334 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 228 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46A50 Compactness in topological linear spaces; angelic spaces, etc. 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) 49S05 Variational principles of physics Keywords:subspaces of Sobolev spaces; symmetries; compactness properties PDF BibTeX XML Cite \textit{P.-L. Lions}, J. Funct. Anal. 49, 315--334 (1982; Zbl 0501.46032) Full Text: DOI References: [1] Berestycki, H.; Lions, P. L., Existence d’ondes solitaires dans des problèmes non linéaires du type Klein-Gordon, C.R. Acad. Sci. Paris, 287, 503-506 (1978) · Zbl 0391.35055 [2] Berestycki, H.; Lions, P. L., Existence d’ondes solitaires dans des problèmes non linéaires du type Klein-Gordon, C.R. Acad. Sci. Paris, 288, 395-398 (1979) · Zbl 0397.35024 [4] Berestycki, H.; Lions, P. L., Existence of a ground state in nonlinear equations of the type Klein-Gordon, (Cottle, R. W.; etal., Variational Inequalities and Complementarity Theory and Applications (1979), Wiley: Wiley New York) · Zbl 0707.35143 [6] Brascamp, H. J.; Lieb, E. H.; Luttinger, J. M., A general rearrangement inequality for multiple integrals, J. Funct. Anal., 17, 227-237 (1974) · Zbl 0286.26005 [7] Coleman, S.; Glazer, V.; Martin, A., Action minima among solutions to a class of Euclidean scalar field equations, Comm. Math. Phys., 58, 211-221 (1978) [10] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inqualities (1952), Cambridge Univ. Press: Cambridge Univ. Press London/New York [11] Lieb, E. H., Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation, Stud. Appl. Math., 57, 93-105 (1977) · Zbl 0369.35022 [12] Lions, J. L.; Magenes, E., (Problèmes aux limites non homogènes et applications, Vol. 1 (1968), Dunod: Dunod Paris) · Zbl 0165.10801 [13] Lions, P. L., The Choquard equation and related questions, Nonlinear Anal. T.M.A., 4, 1063-1073 (1980) · Zbl 0453.47042 [14] Lions, P. L., Minimization problems in \(L^1(R^N)\), J. Funct. Anal., 41, 236-275 (1981) · Zbl 0464.49019 [15] Lions, P. L., A minimization problem in \(L^1\) arising in astrophysics, (Nonlinear Partial Differential Equations and Their Applications. Nonlinear Partial Differential Equations and Their Applications, Collège de France seminar, Vol. II (1982), Pitman: Pitman London) · Zbl 0485.49004 [16] Lions, P. L., Quelques remarques sur la symétrisation de Schwarz, (Nonlinear Partial Differential Equations and Their Applications. Nonlinear Partial Differential Equations and Their Applications, Collège de France seminar, Vol. I (1981), Pitman: Pitman London) · Zbl 0467.35008 [18] Magenes, E., Spazi di interpolazione ed equazioni a derivate parziali, (Atti del VII Congresso del’Unione Matematica Italiana. Atti del VII Congresso del’Unione Matematica Italiana, Genova (1963)) · Zbl 0178.16501 [19] Strauss, W. A., Existence of solitary waves in higher dimensions, Comm. Math. Phys., 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.