Some Inequalities for Superharmonic Functions on Graphs

Potential Analysis

Volumn 6, Issue 2, 1997, Pages 163-181

  Saloff Coste, Laurent ^a  

^a CNRS   (France)

Author keywords

Graphs; Harnack inequality; Quadratic growth; Superharmonic functions

Indexed keywords

EID: 0031508165     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008648421123     Document Type: Article

References (19)

1. Brandt, A.: Estimates for difference quotients of solutions of Poisson type difference equations. Math. Comp. 20 (1996), 473-499.
2. Cheng, S. Y. and Yau, S.-T.: Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math., 28 (1976), 333-354.
3. Colin de Verdière, Y. and Mathéus, F.: (1992) Empilements de cercles et approximations conformes. Actes de la table ronde de géométrie différentielle, en l'honneur de Marcel Berger. Séminaires et Congrés, 1, collection SMF, A. Besse Eds (1996), 253-272.
4. Delmotte, T.: Inégalité de Harnack elliptique sur les graphes. Coll. Math., to appear.
5. Hebisch, W. and Saloff-Coste, L.: Gaussian estimates for Markov chains and random walks on groups. Ann. Prob. 21 (1993), 673-709.
6. Holopainen, I. and Soardi, P.: Strong Liouville theorem for p-harmonic functions on graphs. Preprint 1996.
7. Lawler, G.: Estimates for differences and Harnack inequality for difference operators coming from random walks with symmetric, spatially inhomogeneous increments. Proc. London Math. Soc. 63 (1990), 552-568.
8. Mathéus, F.: Empilements de cercles et représentations conformes: une nouvelle preuve du théoreème de Rodin-Sullivan. L'enseignement mathématique, to appear.
9. Merkov, A.: Second order elliptic equations on graphs. Math. USSR Sbornik, 55 (1986), 493-509.
10. Moser, J.: On Harnack's theorem for elliptic differential equation. Comm. Pure Appl. Math. 14 (1961), 577-591.
11. Rigoli, M., Salvatori, M. and Vignati, M.: Subharmonic functions on graphs. Israel Math. J., to appear, 1995.
12. Rigoli, M., Salvatori, M. and Vignati, M.: A global Harnack inequality on graphs and some related consequences. Preprint, 1995.
13. Rigoli, M., Salvatori, M. and Vignati M.: Liouvilleproperties on graphs. Preprint, 1996.
14. Saloff-Coste, L.: Inequalities for p-superharmonic functions on networks, Rendiconti Sem. Mat. Fis. Milano, to appear, 1996.
15. Schinzel, A.: An analogue of Harnack's inequality for discrete superharmonic functions. Demonstratio Math. 11 (1978), 47-60.
16. Soardi, P. M.: Potential Theory on infinite networks. Lecture Notes in Math., 1590. Springer, 1994.
17. Varopoulos, N.: Potential theory and diffusion on Riemannian manifolds. Conference in harmonic analysis in honor of Antony Zygmund, Wadsworth, Belmont, California, 1983.
18. Woess, W.: Random walks on infinite graphs and groups. Forthcoming book, 1996.
19. Zhou, X. Y.: Green function estimates and their applications to the intersections of symmetric random walks. Stochastic Processes and their Applications 48 (1993), 31-60.