The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Brownian Motion and Harmonic Analysis on Sierpinski Carpets
Open accessAbstract
We consider a class of fractal subsets ofd formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion X and determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.
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Citations
Cites
The Fractal Geometry of Nature
Mandelbrot, B. B., & Wheeler, J. A. (1983) · American Journal of Physics · doi:10.1119/1.13295 · Cited by 21,832
The Fractal Geometry of Nature
Mandelbrot, B. B., & Longley, P. (1982) · CERN Document Server (European Organization for Nuclear Research) · Cited by 7,293
Density of states on fractals : « fractons »
Alexander, S., & Orbach, R. (1982) · Journal de Physique Lettres · doi:10.1051/jphyslet:019820043017062500 · Cited by 2,108
Riesz, F. (1955) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2,001
Havlin, S., & Ben-Avraham, D. (1987) · Advances in Physics · doi:10.1080/00018738700101072 · Cited by 1,808
Lectures on the Coupling Method
Lindvall, T. (1992) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,096
Random Walks and Electric Networks
Doyle, P., & Snell, J. (1984) · Carus Mathematical Monographs · doi:10.5948/upo9781614440222 · Cited by 1,061
Random walks on fractal structures and percolation clusters
Rammal, R., & Toulouse, G. (1983) · Journal de Physique Lettres · doi:10.1051/jphyslet:0198300440101300 · Cited by 968
Havlin, S., & Ben-Avraham, D. (2002) · Advances in Physics · doi:10.1080/00018730110116353 · Cited by 902
On Harnack's theorem for elliptic differential equations
Moser, J. (1961) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160140329 · Cited by 886
Cited by
Stability results for Harnack inequalities
Grigor'yan, A., & Saloff-Coste, L. (2005) · Annales de l'Institut Fourier · doi:10.5802/aif.2116 · Cited by 99
Metadata
- Authors
- Barlow, M. T., & Bass, R. F.
- Venue
- Canadian Journal of Mathematics
- Publisher
- Canadian Mathematical Society
- Published
- 1999-08-01
- Volume
- 51
- Issue
- 4
- Pages
- 673-744
- ISSN
- 0008-414X (ISSN-L)
- 1496-4279
- OpenAlex
- W1991584117
- Cited by
- 298
- References
- 16
- FWCI
- 17.23
- Type
- journal article
- Language
- en
- Open access
- bronze
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