Symétrie et compacité dans les espaces de Sobolev. (French) Zbl 0501.46032

Lions, Pierre-Louis

J. Funct. Anal. 49, 315-334 (1982).

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

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
[3]	{\scH. Berestycki et P. L. Lions}, Non linear scalar fields equations, I and II, à paraître dans Arch. Rat. Mech. Anal.
[4]	Berestycki, H; Lions, P.L, Existence of a ground state in nonlinear equations of the type Klein-Gordon, () · Zbl 0707.35143
[5]	{\scH. Berestycki et P. L. Lions}, travail en préparation.
[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)
[8]	{\scM. J. Esteban}, à paraître dans Nonlinear Anal T.M.A.
[9]	{\scM. J. Esteban et P. L. Lions}, A compactness lemma, à paraître dans Nonlinear Anal. T.M.A.
[10]	Hardy, G.H; Littlewood, J.E; Polya, G, Inqualities, (1952), 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, ()
[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 L1(RN), J. funct. anal., 41, 236-275, (1981)
[15]	Lions, P.L, A minimization problem in L1 arising in astrophysics, ()
[16]	Lions, P.L, Quelques remarques sur la symétrisation de Schwarz, () · Zbl 0467.35008
[17]	{\scP. L. Lions}, travail en préparation.
[18]	Magenes, E, Spazi di interpolazione ed equazioni a derivate parziali, () · Zbl 0178.16501
[19]	Strauss, W.A, Existence of solitary waves in higher dimensions, Comm. math. phys., 55, 149-162, (1977) · Zbl 0356.35028