메뉴 건너뛰기




Volumn 359, Issue 1, 2007, Pages 91-113

The aronsson equation for absolute minimizers of L∞-functionals associated with vector fields satisfying hörmander's condition

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34547164806     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-06-03897-9     Document Type: Article
Times cited : (37)

References (30)
  • 1
    • 0001457134 scopus 로고
    • Extension of functions satisfying Lipschitz conditions.
    • MR0217665 (36:754)
    • G. Aronsson, Extension of functions satisfying Lipschitz conditions. Ark. Mat. 6 (1967) 551-561. MR0217665 (36:754)
    • (1967) Ark. Mat. , vol.6 , pp. 551-561
    • Aronsson, G.1
  • 2
    • 84950356841 scopus 로고
    • yy = 0.
    • MR0237962 (38:6239)
    • yy = 0. Ark. Mat. 7 (1968) 395-425. MR0237962 (38:6239)
    • (1968) Ark. Mat. , vol.7 , pp. 395-425
    • Aronsson, G.1
  • 4
    • 0038379256 scopus 로고    scopus 로고
    • ∞. Nonlinear analysis, differential equa tions and control (Montreal, QC, 1998)
    • MR1695005 (2001c:49045)
    • ∞. Nonlinear analysis, differential equa tions and control (Montreal, QC, 1998), Kluwer Acad. Publ. Dordrecht, 1999 (1-60). MR1695005 (2001c:49045)
    • (1999) Kluwer Acad. Publ. Dordrecht , pp. 1-60
    • Barron, N.1
  • 6
    • 0036381924 scopus 로고    scopus 로고
    • On ∞-harmonic functions on the Heisenberg group
    • MR1900561 (2003g:35033)
    • T. Bieske, On ∞-harmonic functions on the Heisenberg group. Comm. Partial Differential Equations 27 (2002), no.3-4, 727-761. MR1900561 (2003g:35033)
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.3-4 , pp. 727-761
    • Bieske, T.1
  • 7
    • 0036768059 scopus 로고    scopus 로고
    • Viscosity solutions on Grushin-type planes.
    • MR1951247 (2003k:35037)
    • T. Bieske, Viscosity solutions on Grushin-type planes. Illinois J. Math. 46 (2002), no.3, 893-911. MR1951247 (2003k:35037)
    • (2002) Illinois J. Math. , vol.46 , Issue.3 , pp. 893-911
    • Bieske, T.1
  • 8
    • 77951213719 scopus 로고    scopus 로고
    • Lipschitz extension on generalized Grushin type spaces. to appear
    • MR2125531
    • T. Bieske, Lipschitz extension on generalized Grushin type spaces. To appear in Mich. Math. J. MR2125531
    • Mich. Math. J
    • Bieske, T.1
  • 11
    • 0038170019 scopus 로고    scopus 로고
    • An efficient derivation of the aronsson equation
    • MR1981858
    • M. Crandall, An Efficient Derivation of the Aronsson Equation. Arch. Rational Mech. Anal. 167, 2003;4:271-279. MR1981858
    • (2003) Arch. Rational Mech. Anal. , vol.167 , Issue.4 , pp. 271-279
    • Crandall, M.1
  • 12
    • 0002449458 scopus 로고
    • Fully nonlinear elliptic equations
    • AMS, Providence, RI MR1351007 (96h:35046)
    • L. Caffarelli, X. Cabŕe, Fully nonlinear elliptic equations. AMS colloquium publications 43, AMS, Providence, RI, 1995. MR1351007 (96h:35046)
    • (1995) AMS Colloquium Publications , vol.43
    • Caffarelli, L.1    Cabŕe, X.2
  • 14
    • 77951210484 scopus 로고    scopus 로고
    • Southwest Texas State Univ., San Marcos, TX MR1804769 (2001j:35076)
    • Electron. J. Differ. Equ. Conf., 6, Southwest Texas State Univ., San Marcos, TX, 2001. MR1804769 (2001j:35076)
    • (2001) Differ. Equ. Conf. , vol.6
    • Electron., J.1
  • 15
    • 0012678938 scopus 로고    scopus 로고
    • Optimal Lipschitz extensions and the infinity Laplacian
    • MR1861094 (2002h:49048)
    • M. Crandall, L. C. Evans, R. Gariepy, Optimal Lipschitz extensions and the infinity Laplacian. Calc. Var. Partial Differential Equations 13 (2001), no.2, 123-139. MR1861094 (2002h:49048)
    • (2001) Calc. Var. Partial Differential Equations , vol.13 , Issue.2 , pp. 123-139
    • Crandall, M.1    Evans, L.C.2    Gariepy, R.3
  • 16
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • MR1118699 (92j:35050)
    • M. Crandall, H. Ishii, P. L. Lions, User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992), no.1, 1-67. MR1118699 (92j:35050)
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 17
    • 84967758647 scopus 로고
    • Viscosity solutions of Hamilton-Jacobi equations.
    • MR0690039 (85g:35029)
    • M. Crandall, P. L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277 (1983), no.1, 1-42. MR0690039 (85g:35029)
    • (1983) Trans. Amer. Math. Soc. , vol.277 , Issue.1 , pp. 1-42
    • Crandall, M.1    Lions, P.L.2
  • 18
    • 0003379820 scopus 로고
    • Estimates for smooth absolutely minimizing Lipschitz extensions
    • MR1241488 (94k:35117)
    • L. C. Evans, Estimates for smooth absolutely minimizing Lipschitz extensions. Electron. J. Differential Equations 1993, No.03, 9 pp. MR1241488 (94k:35117)
    • (1993) Electron. J. Differential Equations , Issue.3 , pp. 9
    • Evans, L.C.1
  • 20
    • 0001594749 scopus 로고    scopus 로고
    • Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields
    • MR1437714 (98c:49037)
    • B. Franchi, R. Serapioni, F. Serra Cassano, Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields. Houston J. Math. 22 (1996), no.4, 859-890. MR1437714 (98c:49037)
    • (1996) Houston J. Math. , vol.22 , Issue.4 , pp. 859-890
    • Franchi, B.1    Serapioni, R.2    Serra Cassano, F.3
  • 21
    • 0032410775 scopus 로고    scopus 로고
    • Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathodory spaces
    • MR1631642 (2000i:46025)
    • N. Garofalo, D. Nhieu, Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathodory spaces. J. Anal. Math. 74 (1998), 67-97. MR1631642 (2000i:46025)
    • (1998) J. Anal. Math. , vol.74 , pp. 67-97
    • Garofalo, N.1    Nhieu, D.2
  • 22
    • 0346856228 scopus 로고    scopus 로고
    • Sobolev met Poincaŕe
    • x+101 pp. MR1683160 (2000j:46063)
    • P. Hajlasz, P. Koskela, Sobolev met Poincaŕe. Mem. Amer. Math. Soc. 145 (2000), no.688, x+101 pp. MR1683160 (2000j:46063)
    • (2000) Mem. Amer. Math. Soc. , vol.145 , pp. 688
    • Hajlasz, P.1    Koskela, P.2
  • 23
    • 84990575194 scopus 로고
    • On existence and uniqueness of viscosity solutions of fully nonlinear second-order elliptic PDEs
    • MR0973743 (89m:35070)
    • H. Ishii, On existence and uniqueness of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math. 42; 1989:14-45. MR0973743 (89m:35070)
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 14-45
    • Ishii, H.1
  • 24
    • 0003269877 scopus 로고    scopus 로고
    • Minimization problems for Lipschitz functions via viscosity solutions.
    • MR1632063 (2000a:49055)
    • P. Juutinen, Minimization problems for Lipschitz functions via viscosity solutions. Ann. Acad. Sci. Fenn. Math. Diss. No. 115 (1998) MR1632063 (2000a:49055)
    • (1998) Ann. Acad. Sci. Fenn. Math. Diss. , Issue.115
    • Juutinen, P.1
  • 25
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations.
    • MR0920674 (89a:35038)
    • R. Jensen, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations. Arch. Rational Mech. Anal. 101 (1988), no.1, 1-27. MR0920674 (89a:35038)
    • (1988) Arch. Rational Mech. Anal. , vol.101 , Issue.1 , pp. 1-27
    • Jensen, R.1
  • 26
    • 21144476154 scopus 로고
    • Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient.
    • MR1218686 (94g:35063)
    • R. Jensen, Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient. Arch. Rational Mech. Anal. 123 (1993), no.1, 51-74. MR1218686 (94g:35063)
    • (1993) Arch. Rational Mech. Anal. , vol.123 , Issue.1 , pp. 51-74
    • Jensen, R.1
  • 27
    • 84966259849 scopus 로고
    • A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations.
    • MR0934877 (89f:35027)
    • R. Jensen, P. L. Lions, P. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations. Proc. Amer. Math. Soc. 102 (1988), no.4, 975-978. MR0934877 (89f:35027)
    • (1988) Proc. Amer. Math. Soc. , vol.102 , Issue.4 , pp. 975-978
    • Jensen, R.1    Lions, P.L.2    Souganidis, P.3
  • 28
    • 0002408881 scopus 로고
    • The Harnack inequality for ∞-harmonic functions.
    • MR1322829 (96b:35025)
    • P. Lindqvist, J. Manfredi, The Harnack inequality for ∞-harmonic functions. Electron. J. Differential Equations 1995, No.04, 5 pp. MR1322829 (96b:35025)
    • (1995) Electron. J. Differential Equations , Issue.4 , pp. 5
    • Lindqvist, P.1    Manfredi, J.2
  • 30
    • 0041862120 scopus 로고
    • Balls and metrics defined by vector fields. I. Basic properties
    • MR0793239 (86k:46049)
    • A. Nagel, E. Stein, S. Wainger, Balls and metrics defined by vector fields. I. Basic properties. Acta Math. 155 (1985), no.1-2, 103-147. MR0793239 (86k:46049)
    • (1985) Acta Math , vol.155 , Issue.1-2 , pp. 103-147
    • Nagel, A.1    Stein, E.2    Wainger, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.