메뉴 건너뛰기




Volumn 12, Issue 1, 2001, Pages 59-84

Extremal functions for optimal Sobolev inequalities on compact manifolds

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002193410     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005260000044     Document Type: Article
Times cited : (34)

References (29)
  • 1
    • 84972498579 scopus 로고
    • Problèmes isopérimétriques et espaces de Sobolev
    • T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, Journal of Differential Geometry 11 (1976), 573-598
    • (1976) Journal of Differential Geometry , vol.11 , pp. 573-598
    • Aubin, T.1
  • 2
    • 0001676787 scopus 로고
    • Espaces de Sobolev sur les variétés riemanniennes
    • T. Aubin, Espaces de Sobolev sur les variétés riemanniennes, Bulletin des Sciences Mathématiques 100 (1976), 149-173
    • (1976) Bulletin des Sciences Mathématiques , vol.100 , pp. 149-173
    • Aubin, T.1
  • 3
    • 0001596880 scopus 로고
    • Equations différentielles non-linéaires et problème de Yamabe concernant la courbure scalaire
    • T. Aubin, Equations différentielles non-linéaires et problème de Yamabe concernant la courbure scalaire, Journal de Mathématiques Pures et Appliquées 55 (1976), 269-296
    • (1976) Journal de Mathématiques Pures et Appliquées , vol.55 , pp. 269-296
    • Aubin, T.1
  • 5
    • 0032065420 scopus 로고    scopus 로고
    • Best constants in Sobolev inequalities for compact manifolds of nonpositive curvature
    • T. Aubin, O. Druet and E. Hebey, Best constants in Sobolev inequalities for compact manifolds of nonpositive curvature, Comptes Rendus de l'Académie des Sciences de Paris 326 (1998), 1117-1121
    • (1998) Comptes Rendus de l'Académie des Sciences de Paris , vol.326 , pp. 1117-1121
    • Aubin, T.1    Druet, O.2    Hebey, E.3
  • 7
    • 0001039718 scopus 로고    scopus 로고
    • Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
    • D. Bakry and M. Ledoux, Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator, Duke Mathematical Journal 85(1), 1996, 253-270
    • (1996) Duke Mathematical Journal , vol.85 , Issue.1 , pp. 253-270
    • Bakry, D.1    Ledoux, M.2
  • 8
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and Moser-Trüdinger inequality
    • W. Beckner, Sharp Sobolev inequalities on the sphere and Moser-Trüdinger inequality, Annals of mathematics 138 (1993), 213-242
    • (1993) Annals of Mathematics , vol.138 , pp. 213-242
    • Beckner, W.1
  • 9
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Communications on Pure and Applied mathematics 36, 1983, 437-477
    • (1983) Communications on Pure and Applied Mathematics , vol.36 , pp. 437-477
    • Brézis, H.1    Nirenberg, L.2
  • 10
    • 84990617031 scopus 로고
    • Asymptotic symmetry and local behavior of semilinear elliptic equations with Sobolev growth
    • L.A. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with Sobolev growth, Communications on Pure and Applied Mathematics 42 (1989), 271-297
    • (1989) Communications on Pure and Applied Mathematics , vol.42 , pp. 271-297
    • Caffarelli, L.A.1    Gidas, B.2    Spruck, J.3
  • 11
    • 51249180345 scopus 로고
    • A sharp four-dimensional isoperimetric inequality
    • C.B. Croke, A sharp four-dimensional isoperimetric inequality, Comment. Math. Helvitici 59, 1984, 187-192
    • (1984) Comment. Math. Helvitici , vol.59 , pp. 187-192
    • Croke, C.B.1
  • 12
    • 0001511734 scopus 로고    scopus 로고
    • On some nonlinear equations involving the p-laplacian with critical Sobolev growth
    • F. Demengel and E. Hebey, On some nonlinear equations involving the p-laplacian with critical Sobolev growth, Advances in Differential equations, Vol 3, Number 4, 1998, 533-574
    • (1998) Advances in Differential Equations , vol.3 , Issue.4 , pp. 533-574
    • Demengel, F.1    Hebey, E.2
  • 13
    • 0012940545 scopus 로고    scopus 로고
    • Nonlinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds
    • Z. Djadli, Nonlinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds, Calculus of Variations 8, 1999, 293-326
    • (1999) Calculus of Variations , vol.8 , pp. 293-326
    • Djadli, Z.1
  • 14
    • 0001216371 scopus 로고    scopus 로고
    • Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds
    • O. Druet, Optimal Sobolev inequalities of arbitrary order on compact Riemannian manifolds, Journal of Functional Analysis 159, 1998, 217-242
    • (1998) Journal of Functional Analysis , vol.159 , pp. 217-242
    • Druet, O.1
  • 15
    • 0033444350 scopus 로고    scopus 로고
    • The best constants problem in Sobolev inequalities
    • O. Druet, The best constants problem in Sobolev inequalities, Mathematische Annalen 314 (1999), 327-346
    • (1999) Mathematische Annalen , vol.314 , pp. 327-346
    • Druet, O.1
  • 18
    • 38249003092 scopus 로고
    • Courbure scalaire et géométrie conforme
    • E. Hebey, Courbure scalaire et géométrie conforme, Journal of Geometry and Physics 10 (1993), 345-380
    • (1993) Journal of Geometry and Physics , vol.10 , pp. 345-380
    • Hebey, E.1
  • 19
    • 0003228562 scopus 로고    scopus 로고
    • Sobolev Spaces on Riemannian Manifolds
    • Springer-Verlag
    • E. Hebey, Sobolev Spaces on Riemannian Manifolds, Lecture Notes in Mathematics, Springer-Verlag 1635 1996
    • (1996) Lecture Notes in Mathematics , vol.1635
    • Hebey, E.1
  • 20
    • 0032163930 scopus 로고    scopus 로고
    • Fonctions extrémales pour une inégalité de Sobolev optimale dans la classe conforme de la sphère
    • E. Hebey, Fonctions extrémales pour une inégalité de Sobolev optimale dans la classe conforme de la sphère, Journal de Mathématiques Pures et Appliquées 77 (1998), 721-733
    • (1998) Journal de Mathématiques Pures et Appliquées , vol.77 , pp. 721-733
    • Hebey, E.1
  • 21
    • 0003286319 scopus 로고    scopus 로고
    • Nonlinear analysis on manifolds : Sobolev spaces and inequalities
    • Courant Institute of Mathematical Sciences
    • E. Hebey, Nonlinear analysis on manifolds : Sobolev spaces and inequalities, CIMS Lecture Notes, vol. 5, Courant Institute of Mathematical Sciences, 1999
    • (1999) CIMS Lecture Notes , vol.5
    • Hebey, E.1
  • 22
    • 84974004186 scopus 로고
    • The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
    • E. Hebey and M. Vaugon, The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Mathematical Journal 79 (1995), 235-279
    • (1995) Duke Mathematical Journal , vol.79 , pp. 235-279
    • Hebey, E.1    Vaugon, M.2
  • 24
    • 0002154875 scopus 로고
    • An isoperimetric comparison theorem
    • B. Kleiner, An isoperimetric comparison theorem, Inventiones Mathematicae 108 (1992), 37-47
    • (1992) Inventiones Mathematicae , vol.108 , pp. 37-47
    • Kleiner, B.1
  • 25
    • 84980088516 scopus 로고
    • A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations
    • J. Moser, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Communications on Pure and Applied Mathematics 13, 1960
    • (1960) Communications on Pure and Applied Mathematics , vol.13
    • Moser, J.1
  • 26
    • 84972541914 scopus 로고
    • The conjectures on conformal transformations of Riemannian manifolds
    • M. Obata, The conjectures on conformal transformations of Riemannian manifolds, Journal of Differential Geometry 6 (1971), 247-258
    • (1971) Journal of Differential Geometry , vol.6 , pp. 247-258
    • Obata, M.1
  • 27
    • 84972506352 scopus 로고
    • Conformal deformation of a riemannian metric to constant scalar curvature
    • R. Schoen, Conformal deformation of a riemannian metric to constant scalar curvature, Journal of Differential Geometry, 20, 1984, 479-495
    • (1984) Journal of Differential Geometry , vol.20 , pp. 479-495
    • Schoen, R.1
  • 28
    • 34250392866 scopus 로고
    • Best constants in Sobolev inequality
    • G. Talenti, Best constants in Sobolev inequality, Ann. di Matem. Pura ed Appl. 110 (1976), 353-372
    • (1976) Ann. di Matem. Pura ed Appl. , vol.110 , pp. 353-372
    • Talenti, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.