p-harmonic functions on graphs and manifolds

Manuscripta Mathematica

Volumn 94, Issue 1, 1997, Pages 95-110

  Holopainen, Ilkka ^b   Soardi, Paolo M ^a  

^a UNIVERSITY OF MILAN   (Italy)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031227441     PISSN: 00252611     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02677841     Document Type: Article

References (26)

1. Benjamini, I.: Instability of the Liouville property for quasi-isometric graphs and manifolds of polynomial volume growth. J. Theoret. Probab. 4 631-637 (1991)
2. Benjamini, I., Chavel, I., E. Feldman, E.: Heat kernel lower bounds on Riemannian manifolds using the old ideas of Nash. Proc. London Math. Soc. 72 215-240 (1996)
3. Coulhon, T.: Noyau de la chaleur et discrétisation d'une variété riemannienne. Israel J. Math. 80 289-300 (1992)
4. Coulhon, T., Saloff-Coste, L.: Variétés riemanniennes isométriques à l'infini. Rev. Mat. Iberoamericana 11 687-726 (1995)
5. Dodziuk, J.: Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Amer. Math. Soc. 284 787-794 (1984)
6. Grigor'yan, A.: On Liouville theorems for harmonic functions with finite Dirichlet integral. Math. Sb. 132(174) 496-516 (1987) (Russian) [English transl.: Math. USSR Sb. 69 485-504 (1988)]
7. Grigor'yan, A.: On Liouville theorems for harmonic functions with finite Dirichlet integral. Math. Sb. 132(174) 496-516 (1987) (Russian) [English transl.: Math. USSR Sb. 69 485-504 (1988)]
8. Heinonen, J., Kilpeläinen, T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations. (Oxford Mathematical Monographs) Oxford, New York, Tokyo: Clarendon Press 1993
9. Holopainen, I.: Nonlinear potential theory and quasiregular mappings on Riemannian manifolds. Ann. Acad. Sci. Fenn. Ser. AI Math. Diss. 74 1-45 (1990)
10. Holopainen, I.: Positive solutions of quasilinear elliptic equations on Riemannian manifolds. Proc. London Math. Soc. (3) 65 651-672 (1992)
11. Holopainen, I.: Rough isometries and p-harmonic functions with finite Dirichlet integral. Rev. Mat. Iberoamericana 10 143-176 (1994)
12. Holopainen, I.: Solutions of elliptic equations on manifolds with roughly Euclidean ends. Math. Z. 217 459-477 (1994)
13. Kanai, M.: Rough isometries and combinatorial approximations of geometries of non-compact Riemannian manifolds. J. Math. Soc. Japan 37 391-413 (1985)
14. Kanai, M.: Rough isometries and the parabolicity of Riemannian manifolds. J. Math. Soc. Japan 38 227-238 (1986)
15. Kilpeläinen, T., Malý, J.: The Wiener test and potential estimates for quasilinear elliptic equations. Acta Math. 172 137-161 (1994)
16. Lyons, T.: Instability of the Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. J. Differential Geometry 26 33-66 (1987)
17. Lyons, T., Sullivan, D.: Function theory, random paths and covering spaces. J. Differential Geometry 19 299-323 (1984)
18. Markvorsen, S., McGuinness, S., Thomassen, C.: Transient random walks on graphs and metric spaces with applications to hyperbolic surfaces. Proc. London Math. Soc. (3) 64 1-20 (1992)
19. Murakami, A., Yamasaki, M.: Nonlinear potentials on an infinite network. Mem. Fac. Sci. Shimane Univ. 26 15-28 (1992)
20. Soardi, P.M.: Rough isometries and Dirichlet finite harmonic functions on graphs. Proc. Amer. Math. Soc. 119 1239-1248 (1993)
21. Soardi, P.M.: Potential Theory on Infinite Networks (Lecture Notes in Math., vol. 1590) Springer, Berlin Heidelberg New York, 1994
22. Soardi, P.M., Yamasaki, M.: Parabolic index and rough isometries. Hiroshima Math. J. 23 333-342 (1993)
23. Soardi, P.M., Yamasaki, M.: Classification of infinite networks and its application. Circuit Systems Signal Process 12 133-149 (1993)
24. Varopoulos, N.: Brownian motion and random walks on manifolds. Ann. Inst. Fourier (Grenoble) 34 243-269 (1984)
25. Yamasaki, M.: Parabolic and hyperbolic infinite networks. Hiroshima Math. J. 7 135-146 (1977)
26. Yamasaki, M.: Discrete potentials on an infinite network. Mem. Fac. Sci. Shimane Univ. 13 31-44 (1979)