A trace theorem for Dirichlet forms on fractals

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We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields, which behave as the appropriate fractal diffusion within each fractal component of the field.
32 pages, 2 figures

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Probability, Classical Analysis and ODEs, 46E35; 28A80; 31C25; 60J60

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http://salesiana.dossiersoluciones.com/handle/123456789/103813

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510553
 http://arxiv.org/abs/math/0510553
 J. Func. Anal., 238 (2006), 578--611

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arXiv