Inégalité de Harnack elliptique sur les graphes

T. Delmotte

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 1, page 19-37
  • ISSN: 0010-1354

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Delmotte, T.. "Inégalité de Harnack elliptique sur les graphes." Colloquium Mathematicae 72.1 (1997): 19-37. <http://eudml.org/doc/210453>.

@article{Delmotte1997,
author = {Delmotte, T.},
journal = {Colloquium Mathematicae},
keywords = {Harnack inequality; Moser's iteration; strongly local Dirichlet forms},
language = {fre},
number = {1},
pages = {19-37},
title = {Inégalité de Harnack elliptique sur les graphes},
url = {http://eudml.org/doc/210453},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Delmotte, T.
TI - Inégalité de Harnack elliptique sur les graphes
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 1
SP - 19
EP - 37
LA - fre
KW - Harnack inequality; Moser's iteration; strongly local Dirichlet forms
UR - http://eudml.org/doc/210453
ER -

References

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  1. [BCLSC] D. Bakry, T. Coulhon, M. Ledoux and L. Saloff-Coste, Sobolev inequalities in disguise, Indiana Univ. Math. J., à paraître. 
  2. [B] N. Burger, Espace des fonctions à variation moyenne bornée sur un espace de nature homogène, C. R. Acad. Sci. Paris Sér. A 286 (1978), 139-142. Zbl0368.46037
  3. [CKS] E. Carlen, S. Kusuoka and D. Stroock, Upper bounds for symmetric Mar- kov functions, Ann. Inst. H. Poincaré Probab. Statist. 23 (1987), 245-287. Zbl0634.60066
  4. [CSC1] T. Coulhon et L. Saloff-Coste, Puissances d'un opérateur régularisant, ibid. 26 (1990), 419-436. Zbl0709.47042
  5. [CSC2] T. Coulhon et L. Saloff-Coste, Isopérimétrie sur les groupes et les variétés, Rev. Mat. Iberoamericana 9 (1993), 293-314. 
  6. [CW] R. R. Coifman et G. Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Math. 242, Springer, 1971. 
  7. [G] A. A. Grigor'yan, The heat equation on noncompact Riemannian manifolds, Math. USSR-Sb. 72 (1992), 47-77. 
  8. [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. Zbl0102.04302
  9. [L] G. F. Lawler, Estimates for differences and Harnack inequality for difference operators coming from random walks with symmetric, spatially inhomogeneous, increments, Proc. London Math. Soc. (3) 63 (1991), 552-568. Zbl0774.39004
  10. [Me] A. B. Merkov, Second-order elliptic equations on graphs, Math. USSR-Sb. 55 (1986), 493-509. Zbl0657.35044
  11. [Mo1] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591. Zbl0111.09302
  12. [Mo2] J. Moser, A Harnack inequality for parabolic differential equations, ibid. 17 (1964), 101-134. 
  13. [SC1] L. Saloff-Coste, A note on Poincaré, Sobolev and Harnack inequalities, Internat. Math. Res. Notices 1992, no. 2, 27-38. Zbl0769.58054
  14. [SC2] L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Anal. 4 (1995), 429-467. Zbl0840.31006
  15. [V1] N. Varopoulos, Une généralisation du théorème de Hardy-Littlewood-Sobo- lev pour les espaces de Dirichlet, C. R. Acad. Sci. Paris Sér. I 299 (1984), 651-654. Zbl0566.31006
  16. [V2] N. Varopoulos, Fonctions harmoniques sur les groupes de Lie, ibid. 304 (1987), 519-521. 
  17. [Z] X. Y. Zhou, Green function estimates and their applications to the intersections of symmetric random walks, Stochastic Process. Appl. 48 (1993), 31-60. Zbl0810.60064

Citations in EuDML Documents

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  1. Pascal Auscher, Thierry Coulhon, Gaussian lower bounds for random walks from elliptic regularity
  2. Antoine Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations
  3. Antoine Gloria, Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations
  4. Daniel Boivin, Tail estimates for homogenization theorems in random media
  5. Sébastien Blachère, Harmonic functions on annuli of graphs
  6. Thierry Delmotte, Harnack inequalities on graphs

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