메뉴 건너뛰기




Volumn 15, Issue 1, 1999, Pages 181-232

Parabolic Harnack inequality and estimates of Markov chains on graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033481532     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/254     Document Type: Article
Times cited : (242)

References (40)
  • 1
    • 84968488966 scopus 로고
    • Bounds for the fundamental solution of a parabolic equation
    • Aronson, D. G., Bounds for the fundamental solution of a parabolic equation. Bull. Amer. Math. Soc. 73 (1967), 890-896.
    • (1967) Bull. Amer. Math. Soc. , vol.73 , pp. 890-896
    • Aronson, D.G.1
  • 2
    • 0042891550 scopus 로고
    • Theory of minimal surfaces and a counter-example to the Bernstein conjecture in high dimensions
    • New-York University
    • Bombieri, E., Theory of minimal surfaces and a counter-example to the Bernstein conjecture in high dimensions. Mimeographed Notes of Lectures held at Courant Institute. New-York University, 1970.
    • (1970) Mimeographed Notes of Lectures Held at Courant Institute
    • Bombieri, E.1
  • 3
    • 0000478756 scopus 로고
    • A Harnack inequality for homogeneous graphs and subgraphs
    • Chung, F. R. K., Yau S. T., A Harnack inequality for homogeneous graphs and subgraphs. Comm. Anal. Geom. 2 (1994), 628-639.
    • (1994) Comm. Anal. Geom. , vol.2 , pp. 628-639
    • Chung, F.R.K.1    Yau, S.T.2
  • 5
    • 21344490063 scopus 로고
    • Minorations pour les chaînes de Markov unidimensionnelles
    • Coulhon, T., Saloff-Coste, L., Minorations pour les chaînes de Markov unidimensionnelles. Probab. Theor. Relat. Fields 97 (1993), 423-431.
    • (1993) Probab. Theor. Relat. Fields , vol.97 , pp. 423-431
    • Coulhon, T.1    Saloff-Coste, L.2
  • 6
  • 8
    • 84963041987 scopus 로고
    • Large deviations for heat kernels on graphs
    • Davies, E. B., Large deviations for heat kernels on graphs. J. London Math. Soc. 47 (1993), 65-72.
    • (1993) J. London Math. Soc. , vol.47 , pp. 65-72
    • Davies, E.B.1
  • 9
    • 0001877073 scopus 로고    scopus 로고
    • Inégalité de Harnack elliptique sur les graphes
    • Delmotte, T., Inégalité de Harnack elliptique sur les graphes. Colloquium Mathematicum 72 (1997), 19-37.
    • (1997) Colloquium Mathematicum , vol.72 , pp. 19-37
    • Delmotte, T.1
  • 10
    • 0031139001 scopus 로고    scopus 로고
    • Estimations pour les chaînes de Markov réversibles
    • Delmotte, T., Estimations pour les chaînes de Markov réversibles. C. R. Acad. Sci. Paris 324 (1997), 1053-1058.
    • (1997) C. R. Acad. Sci. Paris , vol.324 , pp. 1053-1058
    • Delmotte, T.1
  • 11
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
    • Fabes, E., Stroock, D., A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Rational Mech. Anal. 96 (1986), 327-338.
    • (1986) Arch. Rational Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.1    Stroock, D.2
  • 12
    • 84956103754 scopus 로고
    • The heat equation on noncompact Riemannian manifolds
    • Grigor'yan, A., The heat equation on noncompact Riemannian manifolds. Math. USSR Sb. 72 (1992), 47-77.
    • (1992) Math. USSR Sb. , vol.72 , pp. 47-77
    • Grigor'yan, A.1
  • 13
    • 0030635295 scopus 로고    scopus 로고
    • Gaussian upper bounds for the heat kernel on arbitrary manifolds
    • Grigor'yan, A., Gaussian upper bounds for the heat kernel on arbitrary manifolds. J. Differential Geom. 45 (1997), 33-52.
    • (1997) J. Differential Geom. , vol.45 , pp. 33-52
    • Grigor'yan, A.1
  • 15
    • 0001926819 scopus 로고
    • Gaussian estimates for Markov chains and random walks on groups
    • Hebisch, W., Saloff-Coste, L., Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21 (1993), 673-709.
    • (1993) Ann. Probab. , vol.21 , pp. 673-709
    • Hebisch, W.1    Saloff-Coste, L.2
  • 16
    • 0031471391 scopus 로고    scopus 로고
    • A strong liouville theorem for p-harmonic functions on graphs
    • Holopainen, I., Soardi, P. M., A strong Liouville theorem for p-harmonic functions on graphs. Ann. Acad. Sci. Fennicae Math. 22 (1997), 205-226.
    • (1997) Ann. Acad. Sci. Fennicae Math. , vol.22 , pp. 205-226
    • Holopainen, I.1    Soardi, P.M.2
  • 17
    • 84972555264 scopus 로고
    • The poincaré inequality for vector fields satisfying the Hörmander 's condition
    • Jerison, D., The Poincaré inequality for vector fields satisfying the Hörmander 's condition. Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 19
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • Li, P., Yau, S. T., On the parabolic kernel of the Schrödinger operator. Acta Math. 156 (1986), 153-201.
    • (1986) Acta Math. , vol.156 , pp. 153-201
    • Li, P.1    Yau, S.T.2
  • 20
    • 0006751777 scopus 로고
    • Second-order elliptic equations on graphs
    • Merkov, A. B., Second-order elliptic equations on graphs. Math. USSR Sb. 55 (1986), 493-509.
    • (1986) Math. USSR Sb. , vol.55 , pp. 493-509
    • Merkov, A.B.1
  • 21
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential equations
    • Moser, J., 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
  • 22
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • Moser, J., A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math. 17 (1964), 101-134. Correction in 20 (1967), 231-236.
    • (1964) Comm. Pure Appl. Math. , vol.17 , pp. 101-134
    • Moser, J.1
  • 23
    • 84981758541 scopus 로고
    • Moser, J., A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math. 17 (1964), 101-134. Correction in 20 (1967), 231-236.
    • (1967) Comm. Pure Appl. Math. , vol.20 , pp. 231-236
  • 24
    • 84980178619 scopus 로고
    • On a pointwise estimate for parabolic differential equations
    • Moser, J., On a pointwise estimate for parabolic differential equations. Comm. Pure Appl. Math. 24 (1971), 727-740.
    • (1971) Comm. Pure Appl. Math. , vol.24 , pp. 727-740
    • Moser, J.1
  • 25
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • Nash, J., Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80 (1958), 931-954.
    • (1958) Amer. J. Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 26
    • 84963042087 scopus 로고
    • Heat kernels of graphs
    • Pang, M. M. H., Heat kernels of graphs. J. London Math. Soc. 47 (1993), 50-64.
    • (1993) J. London Math. Soc. , vol.47 , pp. 50-64
    • Pang, M.M.H.1
  • 28
    • 0039314610 scopus 로고    scopus 로고
    • Riesz transforms on graphs for 1 ≤ p ≤ 2
    • Russ, E., Riesz transforms on graphs for 1 ≤ p ≤ 2. To appear in Math. Scandinavia.
    • Math. Scandinavia
    • Russ, E.1
  • 29
    • 84972525827 scopus 로고
    • Uniformly elliptic operators on Riemannian manifolds
    • Saloff-Coste, L., Uniformly elliptic operators on Riemannian manifolds. J. Differential Geom. 36 (1992), 417-450.
    • (1992) J. Differential Geom. , vol.36 , pp. 417-450
    • Saloff-Coste, L.1
  • 30
    • 84963021360 scopus 로고
    • A note on Poincaré, Sobolev and Harnack inequalities
    • Saloff-Coste, L., A note on Poincaré, Sobolev and Harnack inequalities. Internat. Math. Res. Notices 2 (1992), 27-38.
    • (1992) Internat. Math. Res. Notices , vol.2 , pp. 27-38
    • Saloff-Coste, L.1
  • 31
    • 0001586659 scopus 로고
    • Parabolic Harnack inequality for divergence form second order differential operators
    • Saloff-Coste, L., Parabolic Harnack inequality for divergence form second order differential operators. Potential analysis 4 (1995), 429-467.
    • (1995) Potential Analysis , vol.4 , pp. 429-467
    • Saloff-Coste, L.1
  • 33
    • 0037556114 scopus 로고
    • Opérateurs uniformément sous-elliptiques sur les groupes de lie
    • Saloff-Coste, L., Stroock, D., Opérateurs uniformément sous-elliptiques sur les groupes de Lie. J. Funct. Anal. 98 (1991), 97-121.
    • (1991) J. Funct. Anal. , vol.98 , pp. 97-121
    • Saloff-Coste, L.1    Stroock, D.2
  • 34
    • 0031539363 scopus 로고    scopus 로고
    • Markov chain approximations to symmetric diffusions
    • Stroock, D. W., Zheng W., Markov chain approximations to symmetric diffusions. Ann. Inst. H. Poincaré 33 (1997), 619-649.
    • (1997) Ann. Inst. H. Poincaré , vol.33 , pp. 619-649
    • Stroock, D.W.1    Zheng, W.2
  • 35
    • 0001738334 scopus 로고
    • The poisson kernel on positively curved manifolds
    • Varopoulos, N., The Poisson kernel on positively curved manifolds. J. Funct. Anal. 44 (1981), 359-380.
    • (1981) J. Funct. Anal. , vol.44 , pp. 359-380
    • Varopoulos, N.1
  • 36
    • 0040597940 scopus 로고
    • Green's function on positively curved manifolds
    • Varopoulos, N., Green's function on positively curved manifolds. J. Funct. Anal. 45 (1982), 109-118.
    • (1982) J. Funct. Anal. , vol.45 , pp. 109-118
    • Varopoulos, N.1
  • 37
    • 0039412623 scopus 로고
    • Green's function on positively curved manifolds, II
    • Varopoulos, N., Green's function on positively curved manifolds, II. J. Funct. Anal. 49 (1982), 170-176.
    • (1982) J. Funct. Anal. , vol.49 , pp. 170-176
    • Varopoulos, N.1
  • 38
    • 0001598968 scopus 로고
    • Potential theory and diffusion on Riemaniann manifolds
    • Wadsworth Math. Ser., Wadsworth, Belmont, Calif
    • Varopoulos, N., Potential theory and diffusion on Riemaniann manifolds. Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II, Wadsworth Math. Ser., Wadsworth, Belmont, Calif. (1983), 821-837.
    • (1983) Conference on Harmonic Analysis in Honor of Antoni Zygmund , vol.1-2 , pp. 821-837
    • Varopoulos, N.1
  • 39
    • 0001141252 scopus 로고
    • Small time Gaussian estimates of the heat diffusion kernel, Part 1: The semigroup technique
    • Varopoulos, N., Small time Gaussian estimates of the heat diffusion kernel, Part 1: the semigroup technique. Bull. Sci. Math. 113 (1989), 253-277.
    • (1989) Bull. Sci. Math. , vol.113 , pp. 253-277
    • Varopoulos, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.