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Volumn 50, Issue 5, 1997, Pages 449-487

Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries

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EID: 0039500609     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0312(199705)50:5<449::aid-cpa2>3.0.co;2-9     Document Type: Article
Times cited : (73)

References (36)
  • 2
    • 38249034469 scopus 로고
    • Elliptic equations with nearly critical growth
    • Atkinson, F. V., and Peletier, L. A., Elliptic equations with nearly critical growth, J. Differential Equations 70, 1987, pp. 349-365.
    • (1987) J. Differential Equations , vol.70 , pp. 349-365
    • Atkinson, F.V.1    Peletier, L.A.2
  • 3
    • 0001676787 scopus 로고
    • Espaces de Sobolev sur les variétés Riemanniennes
    • Aubin, T., Espaces de Sobolev sur les variétés Riemanniennes, Bull. Sci. Math. (2) 100, 1976, pp. 149-173.
    • (1976) Bull. Sci. Math. (2) , vol.100 , pp. 149-173
    • Aubin, T.1
  • 4
    • 84972498579 scopus 로고
    • Problèmes isopérimétriques et espaces de Sobolev
    • Aubin, T., Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geometry 11, 1976, pp. 573-598.
    • (1976) J. Differential Geometry , vol.11 , pp. 573-598
    • Aubin, T.1
  • 6
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • Beckner, W., Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Ann. of Math. (2) 138, 1993, pp. 213-242.
    • (1993) Ann. of Math. (2) , vol.138 , pp. 213-242
    • Beckner, W.1
  • 7
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second-order elliptic operators in general domains
    • Berestycki, H., Nirenberg, L., and Varadhan, S. R. S., The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47, 1994, pp. 47-92.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 8
    • 0002405776 scopus 로고
    • Sobolev inequalities with remainder terms
    • Brezis, H., and Lieb, E. H., Sobolev inequalities with remainder terms, J. Funct. Anal. 62, 1985, pp. 73-86.
    • (1985) J. Funct. Anal. , vol.62 , pp. 73-86
    • Brezis, H.1    Lieb, E.H.2
  • 9
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • Brezis, H., and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36, 1983, pp. 437-477.
    • (1983) Comm. Pure Appl. Math. , vol.36 , pp. 437-477
    • Brezis, H.1    Nirenberg, L.2
  • 10
    • 0001581738 scopus 로고
    • Asymptotics for elliptic equations involving critical growth
    • Partial Differential Equations and the Calculus of Variations, Birkhäuser Boston, Boston
    • Brezis, H., and Peletier, L. A., Asymptotics for elliptic equations involving critical growth, pp. 149-192 in: Partial Differential Equations and the Calculus of Variations, Vol. I, Progress in Nonlinear Differential Equations and Their Applications No. 1, Birkhäuser Boston, Boston, 1989.
    • (1989) Progress in Nonlinear Differential Equations and Their Applications , vol.1 , Issue.1 , pp. 149-192
    • Brezis, H.1    Peletier, L.A.2
  • 11
    • 0001611867 scopus 로고
    • On the existence of an extremal function for an inequality of J. Moser
    • Carleson, L., and Chang, S. Y. A., On the existence of an extremal function for an inequality of J. Moser, Bull. Sci. Math. 110, 1986, pp. 113-127.
    • (1986) Bull. Sci. Math. , vol.110 , pp. 113-127
    • Carleson, L.1    Chang, S.Y.A.2
  • 13
    • 0001231329 scopus 로고
    • Problèmes de Neumann non linéaires sur les variétés Riemanniennes
    • Cherrier, P., Problèmes de Neumann non linéaires sur les variétés Riemanniennes, J. Funct. Anal. 57, 1984, pp. 154-206.
    • (1984) J. Funct. Anal. , vol.57 , pp. 154-206
    • Cherrier, P.1
  • 14
    • 84990613846 scopus 로고
    • Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate
    • Escobar, J. F., Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate, Comm. Pure Appl. Math. 43, 1990, pp. 857-883.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 857-883
    • Escobar, J.F.1
  • 15
    • 0002416517 scopus 로고
    • Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
    • Escobar, J. F., Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary. Ann. of Math. (2) 136, 1992. pp. 1-50.
    • (1992) Ann. of Math. (2) , vol.136 , pp. 1-50
    • Escobar, J.F.1
  • 16
    • 0001256961 scopus 로고
    • Sharp constant in a Sobolev trace inequality
    • Escobar, J. F., Sharp constant in a Sobolev trace inequality, Indiana Univ. Math. J. 37, 1988, pp. 687-698.
    • (1988) Indiana Univ. Math. J. , vol.37 , pp. 687-698
    • Escobar, J.F.1
  • 18
    • 84903853123 scopus 로고
    • Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
    • Han, Z.-C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 8, 1991, pp. 159-174.
    • (1991) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.8 , pp. 159-174
    • Han, Z.-C.1
  • 19
    • 0001619214 scopus 로고    scopus 로고
    • Optimal Sobolev inequalities on complete Riemannian manifolds with Ricci curvature bounded below and positive injectivity radius
    • Hebey, E., Optimal Sobolev inequalities on complete Riemannian manifolds with Ricci curvature bounded below and positive injectivity radius, Amer. J. Math. 118, 1996, pp. 291-300.
    • (1996) Amer. J. Math. , vol.118 , pp. 291-300
    • Hebey, E.1
  • 20
    • 84974004186 scopus 로고
    • The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
    • Hebey, E., and Vangon, M., The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds, Duke Math. J. 79, 1995, pp. 235-279.
    • (1995) Duke Math. J. , vol.79 , pp. 235-279
    • Hebey, E.1    Vangon, M.2
  • 21
    • 0030356364 scopus 로고    scopus 로고
    • Meilleures constantes dans le théorème d'inclusion de Sobolev
    • Hebey, E., and Vaugon, M., Meilleures constantes dans le théorème d'inclusion de Sobolev, Ann. Inst. H. Poincaré Anal. Non Linéaire 13, 1996, pp. 57-93.
    • (1996) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.13 , pp. 57-93
    • Hebey, E.1    Vaugon, M.2
  • 22
    • 84980167932 scopus 로고
    • Remarks on some quasi-linear elliptic equations
    • Kazdan, J. L., and Warner, F. W., Remarks on some quasi-linear elliptic equations, Comm. Pure Appl. Math. 28, 1975, pp. 567-597.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 567-597
    • Kazdan, J.L.1    Warner, F.W.2
  • 23
    • 0000189862 scopus 로고
    • The Nirenberg problem in a domain with boundary
    • Li, Y.Y., The Nirenberg problem in a domain with boundary, Topol. Methods Nonlinear Anal. 6, 1995, pp. 309-329.
    • (1995) Topol. Methods Nonlinear Anal. , vol.6 , pp. 309-329
    • Li, Y.Y.1
  • 24
    • 0001675486 scopus 로고
    • Prescribing scalar curvature on S″ and related problems, I
    • Li, Y.Y., Prescribing scalar curvature on S″ and related problems, I, J. Differential Equations 120, 1995, pp. 319-410.
    • (1995) J. Differential Equations , vol.120 , pp. 319-410
    • Li, Y.Y.1
  • 25
    • 0041858066 scopus 로고    scopus 로고
    • Prescribing scalar curvature on S″ and related problems, II. Existence and compactness
    • Li, Y.Y., Prescribing scalar curvature on S″ and related problems, II. Existence and compactness, Comm. Pure Appl. Math. 49, 1996, pp. 541-597.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 541-597
    • Li, Y.Y.1
  • 26
    • 84974004811 scopus 로고
    • Uniqueness theorems through the method of moving spheres
    • Li, Y.Y., and Zhu. M., Uniqueness theorems through the method of moving spheres, Duke Math. J. 80, 1995, pp. 383-417.
    • (1995) Duke Math. J. , vol.80 , pp. 383-417
    • Li, Y.Y.1    Zhu, M.2
  • 27
    • 84916181784 scopus 로고
    • Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation
    • Lieb, E. H., Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Appl. Math. 57, 1976/77, pp. 93-105.
    • (1976) Studies in Appl. Math. , vol.57 , pp. 93-105
    • Lieb, E.H.1
  • 28
    • 0000298073 scopus 로고
    • Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
    • Lieb, E. H., Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. 118, 1983, pp. 349-374.
    • (1983) Ann. of Math. , vol.118 , pp. 349-374
    • Lieb, E.H.1
  • 29
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations, the limit case, II
    • Lions, P-L., The concentration-compactness principle in the calculus of variations, The limit case, II, Rev. Mat. Iberoamericana 1, 1985, pp. 145-121.
    • (1985) Rev. Mat. Iberoamericana , vol.1 , pp. 145-1121
    • Lions, P.-L.1
  • 30
    • 0001173833 scopus 로고
    • A sharp form of an inequality by N. Trudinger
    • Moser, J., A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20, 1970/71, pp. 1077-1092.
    • (1970) Indiana Univ. Math. J. , vol.20 , pp. 1077-1092
    • Moser, J.1
  • 31
    • 0002432857 scopus 로고
    • Proof of two conjectures of H. Brézis and L. A. Peletier
    • Rey, O., Proof of two conjectures of H. Brézis and L. A. Peletier, Manuscripta Math. 65, 1989, pp. 19-37.
    • (1989) Manuscripta Math. , vol.65 , pp. 19-37
    • Rey, O.1
  • 32
    • 0001239209 scopus 로고
    • On the number of constant scalar curvature metrics in a conformal class
    • Differential Geometry, Longman Scientific & Technical, Harlow
    • Schoen, R., On the number of constant scalar curvature metrics in a conformal class, pp. 311-320 in: Differential Geometry, Pitman Monographs and Surveys in Pure and Applied Mathematics No. 52, Longman Scientific & Technical, Harlow, 1991.
    • (1991) Pitman Monographs and Surveys in Pure and Applied Mathematics , Issue.52 , pp. 311-320
    • Schoen, R.1
  • 34
    • 34250392866 scopus 로고
    • Best constant in Sobolev inequality
    • Talenti, G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110, 1976, pp. 353-372.
    • (1976) Ann. Mat. Pura Appl. (4) , vol.110 , pp. 353-372
    • Talenti, G.1
  • 35
    • 0000453612 scopus 로고
    • On imbeddings into Orlicz spaces and some applications
    • Trudinger, N., On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17, 1967, pp. 473-483.
    • (1967) J. Math. Mech. , vol.17 , pp. 473-483
    • Trudinger, N.1


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