Brownian motion penetrating fractals. An application of the trace theorem of Besov spaces

DOI10.1006/jfan.1999.3500zbMath0960.31005OpenAlexW206532914MaRDI QIDQ1969490

Takashi Kumagai

Publication date: 17 May 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3500

zbMATH Keywords

capacityBesov spacesDirichlet formsdiffusion processesfractals

Mathematics Subject Classification ID

Dirichlet forms (31C25) Diffusion processes (60J60) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (24)

Besov space and trace theorem on a local field and its application ⋮ A trace theorem for Dirichlet forms on fractals ⋮ Markov processes with darning and their approximations ⋮ Indices of Dirichlet forms ⋮ Upper estimate of martingale dimension for self-similar fractals ⋮ Fractal snowflake domain diffusion with boundary and interior drifts ⋮ A trace theorem for Sobolev spaces on the Sierpinski gasket ⋮ Estimates of the transition densities for the reflected Brownian motion on simple nested fractals ⋮ Semilinear evolution transmission problems across fractal layers ⋮ A uniform trace theorem for Dirichlet forms on Sierpinski fractals ⋮ Semilinear evolution problems with Ventcel-type conditions on fractal boundaries ⋮ Brownian motion on some spaces with varying dimension ⋮ A Dirichlet space associated with consistent networks on the ring of \(p\)-adic integers ⋮ A trace theorem for the Dirichlet form on the Sierpinski gasket ⋮ Fractal theoretic aspects of local field ⋮ On singularity of energy measures on self-similar sets ⋮ Discrete characterisations of Lipschitz spaces on fractals ⋮ Multifractional Markov Processes in Heterogeneous Domains ⋮ Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs ⋮ Fractal reinforcement of elastic membranes ⋮ Heat kernel estimates for stable-like processes on \(d\)-sets. ⋮ Measurable Riemannian structures associated with strong local Dirichlet forms ⋮ The Nagumo equation on self-similar fractal sets. ⋮ Function spaces on fractals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The construction of Brownian motion on the Sierpinski carpet
• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• Upper bounds for symmetric Markov transition functions
• Brownian motion on the Sierpinski gasket
• Transition densities for Brownian motion on the Sierpinski carpet
• Dirichlet forms on fractals: Poincaré constant and resistance
• Estimates of transition densities for Brownian motion of nested fractals
• Dirichlet forms and symmetric Markov processes
• Transition density estimates for diffusion processes on homogeneous random Sierpiński carpets
• Dirichlet forms and Brownian motion penetrating fractals
• Homogenization of nested fractals
• Brownian motion on fractals and function spaces
• Brownian motion on nested fractals
• Brownian Motion and Harmonic Analysis on Sierpinski Carpets
• Besov Spaces on Closed Subsets of ℝ n
• Some function spaces related to the brownian motion on simple nested fractals

This page was built for publication: Brownian motion penetrating fractals. An application of the trace theorem of Besov spaces