Coupling and Harnack inequalities for Sierpiński carpets

DOI10.1090/S0273-0979-1993-00424-5zbMath0782.60017arXivmath/9310225MaRDI QIDQ4275677

Martin T. Barlow, Richard F. Bass

Publication date: 3 March 1994

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9310225

zbMATH Keywords

harmonic functionsSierpinski carpetsSobolev inequalitiesPoincaré inequalitiesHarnack inequalitiesBrownian motion on Sierpinski carpets

Mathematics Subject Classification ID

Transition functions, generators and resolvents (60J35) Probability theory on algebraic and topological structures (60B99)

Related Items (12)

Asymptotically one-dimensional diffusions on the Sierpinski gasket and the \(abc\)-gaskets ⋮ Spectral asymptotics for Laplacians on self-similar sets ⋮ Equidistribution and Brownian motion on the Sierpiński gasket ⋮ Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities ⋮ Hodge-de Rham Theory of K-Forms on Carpet Type Fractals ⋮ Geometry and Laplacian on discrete magic carpets ⋮ Estimates for negative eigenvalues of Schrödinger operators on unbounded fractal spaces ⋮ Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance ⋮ Harnack inequalities: an introduction ⋮ Brownian subordinators and fractional Cauchy problems ⋮ Brownian motion in a Brownian crack ⋮ Resistance forms, quasisymmetric maps and heat kernel estimates

Cites Work

• Unnamed Item
• The construction of Brownian motion on the Sierpinski carpet
• Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
• Hardy-Littlewood theory for semigroups
• Transition densities for Brownian motion on the Sierpinski carpet
• Dirichlet forms on fractals: Poincaré constant and resistance
• Local times for Brownian motion on the Sierpinski carpet
• Isoperimetric constants and estimates of heat kernels of pre Sierpinski carpets
• On the resistance of the Sierpiński carpet

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