메뉴 건너뛰기




Volumn 334, Issue 1, 2006, Pages 199-233

Lipschitz continuity, Aleksandrov theorem and characterizations for H-convex functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 29044443500     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-005-0717-4     Document Type: Article
Times cited : (39)

References (38)
  • 1
    • 0345060039 scopus 로고    scopus 로고
    • Weak differentiability of BV functions on stratified groups
    • Ambrosio, L., Magnani, V.: Weak differentiability of BV functions on stratified groups. Math. Z. 245, 123-153 (2003)
    • (2003) Math. Z. , vol.245 , pp. 123-153
    • Ambrosio, L.1    Magnani, V.2
  • 5
    • 0002299746 scopus 로고    scopus 로고
    • Sub-Riemannian geometry
    • Birkhäuser Verlag, Basel
    • Bellaïche, A., Risler, J.J. eds,: Sub-Riemannian geometry, Progress in Mathematics, 144, Birkhäuser Verlag, Basel, 1996
    • (1996) Progress in Mathematics , vol.144
    • Bellaïche, A.1    Risler, J.J.2
  • 6
    • 0039314072 scopus 로고    scopus 로고
    • On the second order differentiability of convex surfaces
    • Bianchi, G., Colesanti, A., Pucci, C.: On the second order differentiability of convex surfaces. Geom. Dedicata 60, 39-48 (1996)
    • (1996) Geom. Dedicata , vol.60 , pp. 39-48
    • Bianchi, G.1    Colesanti, A.2    Pucci, C.3
  • 7
    • 0036381924 scopus 로고    scopus 로고
    • On ∞-harmonic functions on the Heisenberg group
    • Bieske, T.: On ∞-harmonic functions on the Heisenberg group. Comm. Partial Differential Equations 27(3,4), 727-762 (2002)
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.3-4 , pp. 727-762
    • Bieske, T.1
  • 9
    • 0142194374 scopus 로고    scopus 로고
    • Notions of convexity in Carnot groups
    • Danielli, D., Garofalo, N., Nhieu, D.M.: Notions of convexity in Carnot groups. Comm. Anal. Geom. 11(2), 263-341 (2003)
    • (2003) Comm. Anal. Geom. , vol.11 , Issue.2 , pp. 263-341
    • Danielli, D.1    Garofalo, N.2    Nhieu, D.M.3
  • 10
    • 12344332528 scopus 로고    scopus 로고
    • The theorem of Busemann-Feller-Alexandrov in Carnot groups
    • Danielli, D., Garofalo, N., Nhieu, D.M., Tournier, F.: The theorem of Busemann-Feller-Alexandrov in Carnot groups. Comm. Anal. Geom. 12(4), 853-886 (2004)
    • (2004) Comm. Anal. Geom. , vol.12 , Issue.4 , pp. 853-886
    • Danielli, D.1    Garofalo, N.2    Nhieu, D.M.3    Tournier, F.4
  • 11
    • 0000515079 scopus 로고
    • On second derivatives of convex functions
    • Dudley, R.M.: On second derivatives of convex functions. Math. Scand. 41(1), 159-174 (1977)
    • (1977) Math. Scand. , vol.41 , Issue.1 , pp. 159-174
    • Dudley, R.M.1
  • 12
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • CRC Press, Boca Raton
    • Evans, L.C., Gariepy, R.F.: Measure theory and fine properties of functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 15
    • 0032410775 scopus 로고    scopus 로고
    • Lipschitz continuity, global smooth approximation and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
    • Garofalo, N., Nhieu, D.M.: Lipschitz continuity, global smooth approximation and extension theorems for Sobolev functions in Carnot-Carathéodory spaces. Jour. Anal. Math. 74, 67-97 (1998)
    • (1998) Jour. Anal. Math. , vol.74 , pp. 67-97
    • Garofalo, N.1    Nhieu, D.M.2
  • 16
    • 10844225772 scopus 로고    scopus 로고
    • On the second order derivatives of convex functions on the Heisenberg group
    • Gutirrez, C.E., Montanari, A.: On the second order derivatives of convex functions on the Heisenberg group. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3(2), 349-366 (2004)
    • (2004) Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) , vol.3 , Issue.2 , pp. 349-366
    • Gutirrez, C.E.1    Montanari, A.2
  • 17
    • 0002299742 scopus 로고    scopus 로고
    • Carnot-Carathédory spaces seen from within. Subriemannian Geometry
    • ed. by A. Bellaiche and J. Risler, Birkhausr Verlag, Basel
    • Gromov, M.: Carnot-Carathédory spaces seen from within. Subriemannian Geometry, Progress in Mathematics, 144 ed. by A. Bellaiche and J. Risler, Birkhausr Verlag, Basel, 1996
    • (1996) Progress in Mathematics , vol.144
    • Gromov, M.1
  • 19
    • 0346491065 scopus 로고
    • The structure of Lie groups
    • Hochschild, G.: The structure of Lie groups. Holden-Day, 1965
    • (1965) Holden-Day
    • Hochschild, G.1
  • 22
    • 0003703449 scopus 로고
    • Nonlinear elliptic and parabolic equations of the second order
    • Reidel
    • Krylov, N.V.: Nonlinear elliptic and parabolic equations of the second order. Mathematics and its Applications, Reidel, 1987
    • (1987) Mathematics and Its Applications
    • Krylov, N.V.1
  • 25
    • 18444414008 scopus 로고    scopus 로고
    • Differentiability from Sobolev-Poincaré inequality
    • Magnani, V.: Differentiability from Sobolev-Poincaré inequality. Studia Math. 168(3), 251-272 (2005)
    • (2005) Studia Math. , vol.168 , Issue.3 , pp. 251-272
    • Magnani, V.1
  • 26
    • 0012592396 scopus 로고    scopus 로고
    • Surface measures in Carnot-Carathédory spaces
    • Monti, R., Serra Cassano, F.: Surface measures in Carnot-Carathédory spaces. Calc. Var. 13(3), 339-376 (2001)
    • (2001) Calc. Var. , vol.13 , Issue.3 , pp. 339-376
    • Monti, R.1    Serra Cassano, F.2
  • 27
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields I: Basic properties
    • Nagel, A., Stein, E.M., Wainger, S.: Balls and metrics defined by vector fields I: Basic properties. Acta Math. 155, 103-147 (1985)
    • (1985) Acta Math. , vol.155 , pp. 103-147
    • Nagel, A.1    Stein, E.M.2    Wainger, S.3
  • 28
    • 0001773527 scopus 로고
    • Métriques de Carnot-Carathéodory quasiisométries des espaces symétriques de rang un
    • Pansu, P.: Métriques de Carnot-Carathéodory quasiisométries des espaces symétriques de rang un. Ann. Math. 129, 1-60 (1989)
    • (1989) Ann. Math. , vol.129 , pp. 1-60
    • Pansu, P.1
  • 29
    • 0011334773 scopus 로고
    • Generalized derivatives and differentiability almost everywhere
    • (in Russian)
    • Reshetnyak, Yu.G.: Generalized derivatives and differentiability almost everywhere. Mat. Sb. 75, 323-334 (1968) (in Russian)
    • (1968) Mat. Sb. , vol.75 , pp. 323-334
    • Reshetnyak, Yu.G.1
  • 30
    • 29044435133 scopus 로고    scopus 로고
    • English translation
    • Math. USSR-Sb. 4, 293-302 (English translation)
    • Math. USSR-Sb. , vol.4 , pp. 293-302


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.