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Volumn 318, Issue 3, 2000, Pages 453-516

Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups

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EID: 0034368524     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080000127     Document Type: Article
Times cited : (94)

References (81)
  • 1
    • 84972498579 scopus 로고
    • Problèms isopérimétriques et espaces de Sobolev
    • T. Aubin, Problèms isopérimétriques et espaces de Sobolev, J. Diff. Geometry, 11 (1976), 573-598.
    • (1976) J. Diff. 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, Bull. Sc. Math., 100 (1976), 149-173.
    • (1976) Bull. Sc. Math. , 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, J. Math. Pures et appl., 55 (1976), 269-296.
    • (1976) J. Math. Pures et Appl. , vol.55 , pp. 269-296
    • Aubin, T.1
  • 4
    • 0003872752 scopus 로고
    • Nonlinear analysis on manifolds
    • Springer-Verlag, New York
    • T. Aubin, Nonlinear analysis on manifolds. Monge-Ampère equations, Springer-Verlag, New York, 1982.
    • (1982) Monge-Ampère Equations
    • Aubin, T.1
  • 5
    • 0000376647 scopus 로고
    • Principe du maximum, inégalité de Harnack et unicité du problème de cauchy pour les operateurs elliptique degeneres
    • J. M. Bony, Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les operateurs elliptique degeneres, Ann. Inst. Fourier, Grenoble, 1, 119 (1969), 277-304.
    • (1969) Ann. Inst. Fourier, Grenoble, 1 , vol.119 , pp. 277-304
    • Bony, J.M.1
  • 6
    • 0001425629 scopus 로고
    • Espaces des fonctions a variation moyenne bornée sur une espace de nature homogène
    • N. Burger, Espaces des fonctions a variation moyenne bornée sur une espace de nature homogène, C. R. Acad. Sci. PAris Ser. A-B, 3, 286 (1978), 139-142.
    • (1978) C. R. Acad. Sci. Paris Ser. A-B, 3 , vol.286 , pp. 139-142
    • Burger, N.1
  • 7
    • 0001241250 scopus 로고
    • An imbedding theorem and the Harnack inequality for nonlinear subelliptic equations
    • L. Capogna, D. Danielli, N. Garofalo, An imbedding theorem and the Harnack inequality for nonlinear subelliptic equations, Comm. Part. Diff. Eq., 18 (1993), 1765-1794.
    • (1993) Comm. Part. Diff. Eq. , vol.18 , pp. 1765-1794
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 8
    • 0001189770 scopus 로고
    • The geometric Sobolev embedding for vector fields and the isoperimetric inequality
    • L. Capogna, D. Danielli, N. Garofalo, The geometric Sobolev embedding for vector fields and the isoperimetric inequality, Comm. Anal. and Geom., 2 (1994), 203-215.
    • (1994) Comm. Anal. and Geom. , vol.2 , pp. 203-215
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 9
    • 0000921806 scopus 로고    scopus 로고
    • Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations
    • L. Capogna, D. Danielli, N. Garofalo, Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations, Amer. J. of Math., 118 (1997), 1153-1196.
    • (1997) Amer. J. of Math. , vol.118 , pp. 1153-1196
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 10
    • 0032259664 scopus 로고    scopus 로고
    • NTA domains for Carnot-Carathéodory metrics and a fatou type theorem
    • L. Capogna, N. Garofalo, NTA domains for Carnot-Carathéodory metrics and a Fatou type theorem, J. Fourier Anal. Appl., 4, 4-5 (1998), 403-432.
    • (1998) J. Fourier Anal. Appl., 4 , vol.4-5 , pp. 403-432
    • Capogna, L.1    Garofalo, N.2
  • 11
    • 0032325214 scopus 로고    scopus 로고
    • A version of a theorem of Dahlberg for the sub-elliptic Dirichlet problem
    • L. Capogna, N. Garofalo, Duy-Minh Nhieu, A version of a theorem of Dahlberg for the sub-elliptic Dirichlet problem, Math. Res. Letters, 5 (1998), 541-549.
    • (1998) Math. Res. Letters , vol.5 , pp. 541-549
    • Capogna, L.1    Garofalo, N.2    Nhieu, D.-M.3
  • 14
    • 0000133815 scopus 로고
    • Weighted norm inequalities for maximal functions and singular integrals
    • Coifman, C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241-250.
    • (1974) Studia Math. , vol.51 , pp. 241-250
    • Coifman1    Fefferman, C.2
  • 16
    • 0038921437 scopus 로고
    • Harmonic analysis on Heisenberg type groups from a geometric viewpoint
    • "Lie Group Representation III". Springer-Verlag
    • M. Cowling, A. Koranyi, Harmonic analysis on Heisenberg type groups from a geometric viewpoint, in "Lie Group Representation III", pp.60-100, Lec. Notes in Math., 1077 (1984), Springer-Verlag.
    • (1984) Lec. Notes in Math. , vol.1077 , pp. 60-100
    • Cowling, M.1    Korányi, A.2
  • 17
    • 0002171569 scopus 로고
    • Subadditivity of homogeneous norms on certain nilpotent Lie groups
    • J. Cygan, Subadditivity of homogeneous norms on certain nilpotent Lie groups. Proc. Amer. Math. Soc., 83 (1981), 69-70.
    • (1981) Proc. Amer. Math. Soc. , vol.83 , pp. 69-70
    • Cygan, J.1
  • 18
    • 84968515066 scopus 로고
    • Harmonic functions on semidirect extensions of type H nilpotent groups
    • E. Damek, Harmonic functions on semidirect extensions of type H nilpotent groups, Trans. Amer. Math. Soc., 1, 290 (1985), 375-384.
    • (1985) Trans. Amer. Math. Soc., 1 , vol.290 , pp. 375-384
    • Damek, E.1
  • 19
    • 0000632811 scopus 로고
    • A poisson kernel on Heisenberg type nilpotent groups
    • E. Damek, A Poisson kernel on Heisenberg type nilpotent groups, Coll. Math., 53 (1987), 255-268.
    • (1987) Coll. Math. , vol.53 , pp. 255-268
    • Damek, E.1
  • 20
    • 0000632811 scopus 로고
    • The geometry of semi-direct extensions of a Heisenberg type nilpotent group
    • E. Damek, The geometry of semi-direct extensions of a Heisenberg type nilpotent group. Coll. Math., 53 (1987), 255-268.
    • (1987) Coll. Math. , vol.53 , pp. 255-268
    • Damek, E.1
  • 21
    • 0009876165 scopus 로고    scopus 로고
    • Geometric properties of solutions to subelliptic equations in nilpotent Lie groups
    • "Reaction Diffusion Systems", Trieste. October 1995, Ed. G. Caristi Invernizzi, E. Mitidieri, Marcel Dekker
    • D. Danielli, N. Garofalo, Geometric properties of solutions to subelliptic equations in nilpotent Lie groups, Lect. Notes in Pure and Appl. Math., "Reaction Diffusion Systems", Trieste. October 1995, Ed. G. Caristi Invernizzi, E. Mitidieri, Marcel Dekker, 194 (1998).
    • (1998) Lect. Notes in Pure and Appl. Math. , vol.194
    • Danielli, D.1    Garofalo, N.2
  • 22
    • 0003090595 scopus 로고
    • Un problème aux limites pour une classe d'opérateurs du second ordre hypoelliptiques
    • M. Derridj, Un problème aux limites pour une classe d'opérateurs du second ordre hypoelliptiques, Ann. Inst. Fourier, Grenoble, 21, 4 (1971), 99-148.
    • (1971) Ann. Inst. Fourier, Grenoble , vol.21 , Issue.4 , pp. 99-148
    • Derridj, M.1
  • 23
    • 0009833137 scopus 로고
    • Sur un théorème de traces
    • M. Derridj, Sur un théorème de traces, Ann. Inst. Fourier, Grenoble, 22, 2 (1972), 73-83.
    • (1972) Ann. Inst. Fourier, Grenoble , vol.22 , Issue.2 , pp. 73-83
    • Derridj, M.1
  • 25
    • 84968464934 scopus 로고
    • A fundamental solution for a subelliptic operator
    • G. Folland, A fundamental solution for a subelliptic operator. Bull. Amer. Math. Soc., 79 (1973), 373-376.
    • (1973) Bull. Amer. Math. Soc. , vol.79 , pp. 373-376
    • Folland, G.1
  • 26
    • 0000876740 scopus 로고
    • Subelliptic estimates and function spaces on nilpotent Lie groups
    • G. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Math., 13 (1975), 161-207.
    • (1975) Ark. Math. , vol.13 , pp. 161-207
    • Folland, G.1
  • 28
    • 0001077590 scopus 로고
    • Weighted Sobolev-Poincaré inequalities for Grushin type operators
    • B. Franchi, C. Gutierrez, R. L. Wheeden, Weighted Sobolev-Poincaré inequalities for Grushin type operators. Comm. PDE, 19 (1994), 523-604.
    • (1994) Comm. PDE , vol.19 , pp. 523-604
    • Franchi, B.1    Gutierrez, C.2    Wheeden, R.L.3
  • 30
    • 0000422319 scopus 로고
    • Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation
    • N. Garofalo, E. Lanconelli, Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation, Ann. Inst. Fourier (Grenoble), 40 (1990), no. 2, 313-356.
    • (1990) Ann. Inst. Fourier (Grenoble) , vol.40 , Issue.2 , pp. 313-356
    • Garofalo, N.1    Lanconelli, E.2
  • 31
    • 0002739785 scopus 로고
    • Existence and non-existence results for semilinear elliptic problems in unbounded domains
    • N. Garofalo, E. Lanconelli, Existence and non-existence results for semilinear elliptic problems in unbounded domains, Indiana Univ. Math. J., 41 (1992) 71-98.
    • (1992) Indiana Univ. Math. J. , vol.41 , pp. 71-98
    • Garofalo, N.1    Lanconelli, E.2
  • 32
    • 0030488404 scopus 로고    scopus 로고
    • Isoperimetric and sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces
    • N. Garofalo, D. M. Nhieu, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, Comm. Pure Appl. Math., 49 (1996), 1081-1144.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 1081-1144
    • Garofalo, N.1    Nhieu, D.M.2
  • 33
    • 0032410775 scopus 로고    scopus 로고
    • Lipschitz continuity, global smooth approximations and extension theorems for sobolev functions in Carnot-Carathéodory spaces
    • N. Garofalo, D. M. Nhieu, Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces, J. d'Analyse Math., 74 (1998), 67-97.
    • (1998) J. d'Analyse Math. , vol.74 , pp. 67-97
    • Garofalo, N.1    Nhieu, D.M.2
  • 34
    • 0040699077 scopus 로고    scopus 로고
    • The non-linear Dirichlet problem and the CR Yamabe problem
    • Catania, November 12-14 To appear in Le Matematiche
    • N. Garofalo, D. Vassilev, The non-linear Dirichlet problem and the CR Yamabe problem. Proc. of the Conference in memory of Filippo Chiarenza, Catania, November 12-14 1998. To appear in Le Matematiche.
    • (1998) Proc. of the Conference in Memory of Filippo Chiarenza
    • Garofalo, N.1    Vassilev, D.2
  • 36
    • 0031475170 scopus 로고    scopus 로고
    • Nonexistence of weak solutions of nonlinear elliptic equations in exterior domains
    • T. Hashimoto, M. Otani, Nonexistence of weak solutions of nonlinear elliptic equations in exterior domains, Houston J. Math., 2, 23 (1997), 267-290.
    • (1997) Houston J. Math., 2 , vol.23 , pp. 267-290
    • Hashimoto, T.1    Otani, M.2
  • 37
    • 84962991764 scopus 로고
    • Positive solutions of quasilinear elliptic equations on riemannian manifolds
    • no. 3
    • I. Holopainen, Positive solutions of quasilinear elliptic equations on Riemannian manifolds, Proc. London Math. Soc., (3) 65 (1992), no. 3, 651-672.
    • (1992) Proc. London Math. Soc. , vol.65 , Issue.3 , pp. 651-672
    • Holopainen, I.1
  • 38
    • 0013077071 scopus 로고
    • Quasiregular mappings of the Heisenberg group
    • I. Holopainen, S. Rickman, Quasiregular mappings of the Heisenberg group, Math. Ann., 294 (1992), no. 4, 625-643.
    • (1992) Math. Ann. , vol.294 , Issue.4 , pp. 625-643
    • Holopainen, I.1    Rickman, S.2
  • 39
    • 15244346736 scopus 로고
    • Hypoelliptic second-order differential equations
    • H. Hörmander, Hypoelliptic second-order differential equations, Acta Math., 119 (1967), 147-171.
    • (1967) Acta Math. , vol.119 , pp. 147-171
    • Hörmander, H.1
  • 40
    • 0039513848 scopus 로고
    • The poisson space of the Korányi ball
    • H. Hueber, The Poisson space of the Korányi ball, Math. Ann., 268 (1984), no. 2, 223-232.
    • (1984) Math. Ann. , vol.268 , Issue.2 , pp. 223-232
    • Hueber, H.1
  • 41
    • 84972555264 scopus 로고
    • The poincaré inequality for vector fields satisfying Hörmander's condition
    • D. Jerison, The Poincaré inequality for vector fields satisfying Hörmander's condition, Duke Math. J., 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 42
    • 0001214547 scopus 로고
    • The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, I
    • D. Jerison, The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, I, J. of Funct. Anal. 43 (1981), 97-141.
    • (1981) J. of Funct. Anal. , vol.43 , pp. 97-141
    • Jerison, D.1
  • 43
    • 0001214546 scopus 로고
    • The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, II
    • D. Jerison, The Dirichlet problem for the Kohn Laplacian on the Heisenberg group, II, J. of Funct. Anal. 43 (1981), 224-257.
    • (1981) J. of Funct. Anal. , vol.43 , pp. 224-257
    • Jerison, D.1
  • 44
    • 0009323638 scopus 로고
    • A subelliptic, nonlinear eigenvalue problem and scalar curvature on C R manifolds
    • D. Jerison, J. Lee, A subelliptic, nonlinear eigenvalue problem and scalar curvature on C R manifolds, Contemporary Math., 27 (1984), 57-63.
    • (1984) Contemporary Math. , vol.27 , pp. 57-63
    • Jerison, D.1    Lee, J.2
  • 45
    • 84972529948 scopus 로고
    • The Yamabe problem on C R manifolds
    • D. Jerison, J. Lee, The Yamabe problem on C R manifolds, J. Diff. Eq., 25 (1987), 167-197.
    • (1987) J. Diff. Eq. , vol.25 , pp. 167-197
    • Jerison, D.1    Lee, J.2
  • 46
    • 84968516099 scopus 로고
    • Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem
    • D. Jerison, J. Lee, Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. of the Amer. Math. Soc., 1, 1 (1988), 1-13.
    • (1988) J. of the Amer. Math. Soc., 1 , vol.1 , pp. 1-13
    • Jerison, D.1    Lee, J.2
  • 47
    • 84972538885 scopus 로고
    • Intrinsic CR normal coordinates and the CR Yamabe problem
    • D. Jerison, J. Lee, Intrinsic CR normal coordinates and the CR Yamabe problem, J. Diff. Geom., 29 (1989), no. 2, 303-343.
    • (1989) J. Diff. Geom. , vol.29 , Issue.2 , pp. 303-343
    • Jerison, D.1    Lee, J.2
  • 48
    • 0000841192 scopus 로고
    • Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms
    • A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc., 258 (1980), 147-153.
    • (1980) Trans. Amer. Math. Soc. , vol.258 , pp. 147-153
    • Kaplan, A.1
  • 49
    • 0000262219 scopus 로고
    • Riemannian nilmanifolds attached to Clifford modules
    • A. Kaplan, Riemannian nilmanifolds attached to Clifford modules, Geom. Dedicata, 11 (1981), 127-136.
    • (1981) Geom. Dedicata , vol.11 , pp. 127-136
    • Kaplan, A.1
  • 50
    • 33751129464 scopus 로고
    • On the geometry of groups of Heisenberg type
    • A. Kaplan, On the geometry of groups of Heisenberg type, Bull. London Math. Soc., 15 (1983), 35-42.
    • (1983) Bull. London Math. Soc. , vol.15 , pp. 35-42
    • Kaplan, A.1
  • 51
    • 0001647489 scopus 로고
    • Harmonic ananlysis on groups of Heisenberg type
    • "Harmonic Analysis", Springer-Verlag
    • A. Kaplan, F. Ricci, Harmonic ananlysis on groups of Heisenberg type, in "Harmonic Analysis", pp.416-435, Lee. Notes in Math., 992 (1983), Springer-Verlag.
    • (1983) Lee. Notes in Math. , vol.992 , pp. 416-435
    • Kaplan, A.1    Ricci, F.2
  • 53
    • 42549172909 scopus 로고
    • Kelvin transform and harmonic polynomials on the Heisenberg group
    • A. Korányi, Kelvin transform and harmonic polynomials on the Heisenberg group, Adv.Math. 56 (1985), 28-38.
    • (1985) Adv.Math. , vol.56 , pp. 28-38
    • Korányi, A.1
  • 54
    • 42549172909 scopus 로고
    • Geometric properties of Heisenberg-type groups
    • A. Korányi, Geometric properties of Heisenberg-type groups, Adv.Math. 56 (1985), 28-38.
    • (1985) Adv.Math. , vol.56 , pp. 28-38
    • Korányi, A.1
  • 56
    • 0002095644 scopus 로고
    • Horizontal normal vectors and conformal capacity of spherical rings in the Heisenberg group
    • A. Korányi, H. M. Reimann, Horizontal normal vectors and conformal capacity of spherical rings in the Heisenberg group, Bull. Sc. Math., 111 (1987), 3-21.
    • (1987) Bull. Sc. Math. , vol.111 , pp. 3-21
    • Korányi, A.1    Reimann, H.M.2
  • 57
    • 0001022406 scopus 로고    scopus 로고
    • On the poisson kernel for the Kohn Laplacian
    • E. Lanconelli, F. Uguzzoni, On the Poisson kernel for the Kohn Laplacian, Rend. Mat. Appl., 717 (1998), no.4, 659-677.
    • (1998) Rend. Mat. Appl. , vol.717 , Issue.4 , pp. 659-677
    • Lanconelli, E.1    Uguzzoni, F.2
  • 58
    • 0001290613 scopus 로고    scopus 로고
    • Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group
    • E. Lanconelli, F. Uguzzoni, Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group. Boll. Un. Mat. Ital., (8) 1-B (1998), 139-168.
    • (1998) Boll. Un. Mat. Ital. , vol.1 B , Issue.8 , pp. 139-168
    • Lanconelli, E.1    Uguzzoni, F.2
  • 60
    • 85030707196 scopus 로고
    • The concentration compactness principle in the calculus of variations. The locally compact case. Part 1
    • P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part 1, Ann. Inst. H. Poincaré, 1 (1984), 109-145
    • (1984) Ann. Inst. H. Poincaré , vol.1 , pp. 109-145
    • Lions, P.L.1
  • 61
    • 85030719142 scopus 로고
    • The concentration compactness principle in the calculus of variations. The locally compact case. Part 2
    • P. L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part 2. Ann. Inst. H. Poincaré, 1 (1984), 223-283
    • (1984) Ann. Inst. H. Poincaré , vol.1 , pp. 223-283
    • Lions, P.L.1
  • 62
    • 0001294182 scopus 로고
    • The concentration compactness principle in the calculus of variations. The limit case. Part 1
    • 1.1
    • P. L. Lions, The concentration compactness principle in the calculus of variations. The limit case. Part 1, Rev. Mat. Iberoamericana 1.1 (1985), 145-201
    • (1985) Rev. Mat. Iberoamericana , pp. 145-201
    • Lions, P.L.1
  • 63
    • 0001294182 scopus 로고
    • The concentration compactness principle in the calculus of variations. The limit case. Part 2
    • 1.2
    • P. L. Lions, The concentration compactness principle in the calculus of variations. The limit case. Part 2, Rev. Mat. Iberoamericana 1.2 (1985), 45-121
    • (1985) Rev. Mat. Iberoamericana , pp. 45-121
    • Lions, P.L.1
  • 64
    • 0001207007 scopus 로고
    • Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
    • G. Lu, Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications, Rev. Mat. Iberoamericana, 8 (1992), no. 3, 367-439.
    • (1992) Rev. Mat. Iberoamericana , vol.8 , Issue.3 , pp. 367-439
    • Lu, G.1
  • 65
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential equations
    • J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math.14 (1961), 577-591.
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 577-591
    • Moser, J.1
  • 66
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields I: Basic properties
    • A. Nagel, E.M. Stein, S. Wainger, Balls and metrics defined by vector fields I: Basic properties, Acta Math. 155 (1985), 103-147.
    • (1985) Acta Math. , vol.155 , pp. 103-147
    • Nagel, A.1    Stein, E.M.2    Wainger, S.3
  • 67
    • 0000514956 scopus 로고
    • Eigenfunctions of the equation Δu + λf(u) = 0
    • S. Pohožaev, Eigenfunctions of the equation Δu + λf(u) = 0, Soviet Math. Dokl., 6 (1965), 1408-1411.
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 1408-1411
    • Pohožaev, S.1
  • 68
    • 0000494186 scopus 로고
    • Darstellung der Eigenwerte von Au + λu durch ein Randintegral
    • F. Rellich, Darstellung der Eigenwerte von Au + λu durch ein Randintegral, Math. Zeit., 46 (1940), 635-646.
    • (1940) Math. Zeit. , vol.46 , pp. 635-646
    • Rellich, F.1
  • 69
    • 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, J. Differential Geom. 20 (1984), no. 2, 479-495.
    • (1984) J. Differential Geom. , vol.20 , Issue.2 , pp. 479-495
    • Schoen, R.1
  • 70
    • 0000798567 scopus 로고
    • Local behavior of solutions of quasi-linear equations
    • J. Serrin, Local behavior of solutions of quasi-linear equations, Acta Math., 111 (1964). 247-302.
    • (1964) Acta Math. , vol.111 , pp. 247-302
    • Serrin, J.1
  • 71
    • 0000708617 scopus 로고
    • Isolated singularities of solutions of quasi-linear equations
    • J. Serrin, Isolated singularities of solutions of quasi-linear equations, Acta Math., 113 (1965), 219-240.
    • (1965) Acta Math. , vol.113 , pp. 219-240
    • Serrin, J.1
  • 72
    • 0038019332 scopus 로고
    • Some problems in harmonic analysis suggested by symmetric spaces and semisimple groups
    • Gauthier-Villars, Paris
    • E. M. Stein, Some problems in harmonic analysis suggested by symmetric spaces and semisimple groups, Proc. Int. Congr. Math., Nice I, 1970, Gauthier-Villars, Paris, 1971, 173-179.
    • (1970) Proc. Int. Congr. Math., Nice I , pp. 173-179
    • Stein, E.M.1
  • 75
    • 34250392866 scopus 로고
    • Best constant in the Sobolev inequality
    • G. Talenti, Best constant in the Sobolev inequality, Ann. Mat. Pura e Appl., 110 (1976), 353-372.
    • (1976) Ann. Mat. Pura e Appl. , vol.110 , pp. 353-372
    • Talenti, G.1
  • 76
    • 0000471156 scopus 로고
    • Remarks concerning the conformal deformation of Riemannian structures on compact manifolds
    • N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 265-274.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 265-274
    • Trudinger, N.1
  • 79
    • 85016916496 scopus 로고    scopus 로고
    • Ph. D. Dissertation, Purdue University
    • D. Vassilev, Ph. D. Dissertation, Purdue University.
    • Vassilev, D.1
  • 80
    • 0001368413 scopus 로고
    • Subelliptic variational problems
    • C. J. Xu, Subelliptic variational problems, Bull. Soc. Math. France, 118 (1990), 147-169.
    • (1990) Bull. Soc. Math. France , vol.118 , pp. 147-169
    • Xu, C.J.1
  • 81
    • 0033197184 scopus 로고    scopus 로고
    • The dirichlet problems for a class of semilinear sub-elliptic equations
    • C. J. Xu, The Dirichlet problems for a class of semilinear sub-elliptic equations, Nonlinear Anal., 37 (1999), 1039-1049.
    • (1999) Nonlinear Anal. , vol.37 , pp. 1039-1049
    • Xu, C.J.1


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