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Volumn 16, Issue 2, 2002, Pages 151-168

Graphs between the elliptic and parabolic Harnack inequalities

Author keywords

Graph; Harnack inequality

Indexed keywords


EID: 0036116964     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1012632229879     Document Type: Article
Times cited : (22)

References (31)
  • 2
    • 0033465207 scopus 로고    scopus 로고
    • Brownian motion and harmonic analysis on Sierpinski carpets
    • Barlow, M. T. and Bass, R. F.: 'Brownian motion and harmonic analysis on Sierpinski carpets', Canad. J. Math. 51 (1999), 673-744.
    • (1999) Canad. J. Math. , vol.51 , pp. 673-744
    • Barlow, M.T.1    Bass, R.F.2
  • 5
    • 22644452019 scopus 로고    scopus 로고
    • Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
    • Bourdon, M. and Pajot, H.: 'Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings', Proc. Amer. Math. Soc. 127 (1999), 2315-2324.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 2315-2324
    • Bourdon, M.1    Pajot, H.2
  • 6
    • 84980189206 scopus 로고
    • Differential equations on Riemannian manifolds and their geometric applications
    • Cheng, S. and Yau, S. T.: 'Differential equations on Riemannian manifolds and their geometric applications', Comm. Pure Appl. Math. 28 (1975), 333-354.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 333-354
    • Cheng, S.1    Yau, S.T.2
  • 7
    • 0001691206 scopus 로고
    • Isopérimétrie sur les groupes et les variétés
    • Coulhon, T. and Saloff-Coste, L.: 'Isopérimétrie sur les groupes et les variétés', Rev. Mat. Iberoamericana 9 (1993), 293-314.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , pp. 293-314
    • Coulhon, T.1    Saloff-Coste, L.2
  • 8
    • 0001877073 scopus 로고    scopus 로고
    • Inégalité de Harnack elliptique sur les graphes
    • Delmotte, T: 'Inégalité de Harnack elliptique sur les graphes', Coll. Math. 72(1) (1997), 19-37.
    • (1997) Coll. Math. , vol.72 , Issue.1 , pp. 19-37
    • Delmotte, T.1
  • 9
    • 0033481532 scopus 로고    scopus 로고
    • Parabolic Harnack inequality and estimates of Markov chains on graphs
    • Delmotte, T: 'Parabolic Harnack inequality and estimates of Markov chains on graphs', Rev. Mat. Iberoamericana 15(1) (1999), 181-232.
    • (1999) Rev. Mat. Iberoamericana , vol.15 , Issue.1 , pp. 181-232
    • Delmotte, T.1
  • 11
    • 0002740591 scopus 로고
    • Geometric bounds for eigenvalues of Markov chains
    • Diaconis, P. and Stroock, D.: 'Geometric bounds for eigenvalues of Markov chains', Ann. Appl. Probab. 1 (1991), 39-61.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 39-61
    • Diaconis, P.1    Stroock, D.2
  • 13
    • 0002209819 scopus 로고
    • The heatequation on noncompact Riemannian manifolds
    • Russian
    • Grigor'yan, A.: 'The heat equation on noncompact Riemannian manifolds', Mat. Sb. 182(1) (1991), 55-87 (Russian). Math. USSR-Sb. 72 (1992), 47-77 (English translation).
    • (1991) Mat. Sb. , vol.182 , Issue.1 , pp. 55-87
    • Grigor'yan, A.1
  • 14
    • 84956103754 scopus 로고
    • English translation
    • Grigor'yan, A.: 'The heat equation on noncompact Riemannian manifolds', Mat. Sb. 182(1) (1991), 55-87 (Russian). Math. USSR-Sb. 72 (1992), 47-77 (English translation).
    • (1992) Math. USSR-Sb. , vol.72 , pp. 47-77
  • 15
    • 0033245886 scopus 로고    scopus 로고
    • Heat kernel on connected sums of Riemannian manifolds
    • Grigor'yan, A. and Saloff-Coste, L.: 'Heat kernel on connected sums of Riemannian manifolds', Math. Res. Lett. 6 (1999), 307-321.
    • (1999) Math. Res. Lett. , vol.6 , pp. 307-321
    • Grigor'yan, A.1    Saloff-Coste, L.2
  • 17
    • 85009821115 scopus 로고    scopus 로고
    • Thirty-three yes or no questions about mappings, measures, and metrics
    • Heinonen, J. and Semmes, S.: 'Thirty-three yes or no questions about mappings, measures, and metrics', Conform. Geom. Dyn. 1(1) (1997), 1-12.
    • (1997) Conform. Geom. Dyn. , vol.1 , Issue.1 , pp. 1-12
    • Heinonen, J.1    Semmes, S.2
  • 18
    • 0031471391 scopus 로고    scopus 로고
    • A strong Liouville theorem for p-harmonic functions on graphs
    • Holopainen, I. and Soardi, P. M.: 'A strong Liouville theorem for p-harmonic functions on graphs', Ann. Acad. Sci. Fenn. Math. 22 (1997), 205-226.
    • (1997) Ann. Acad. Sci. Fenn. Math. , vol.22 , pp. 205-226
    • Holopainen, I.1    Soardi, P.M.2
  • 19
    • 0029690374 scopus 로고    scopus 로고
    • Transition probabilities for the simple random walk on the Sierpinski graph
    • Jones, O. D.: 'Transition probabilities for the simple random walk on the Sierpinski graph', Stochastic Process Appl. 61 (1996), 45-69.
    • (1996) Stochastic Process Appl. , vol.61 , pp. 45-69
    • Jones, O.D.1
  • 20
    • 0000367213 scopus 로고
    • Subdiffusive behavior of random walk on a random cluster
    • Kesten, H.: 'Subdiffusive behavior of random walk on a random cluster', Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), 425-487.
    • (1986) Ann. Inst. H. Poincaré Probab. Statist. , vol.22 , pp. 425-487
    • Kesten, H.1
  • 22
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • Li, P. and 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
  • 24
    • 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
  • 25
    • 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
  • 26
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • Correction in 20 (1967), 231-236
    • 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
  • 27
    • 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
  • 29
    • 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
  • 30
    • 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 Anal. 4(4) (1995), 429-467.
    • (1995) Potential Anal. , vol.4 , Issue.4 , pp. 429-467
    • Saloff-Coste, L.1
  • 31
    • 0000245433 scopus 로고
    • Sur une courbe dont tout point est un point de ramification
    • Sierpinski, W.: 'Sur une courbe dont tout point est un point de ramification', C.R. Acad. Sci. Paris 162 (1916), 629-632.
    • (1916) C.R. Acad. Sci. Paris , vol.162 , pp. 629-632
    • Sierpinski, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.