A trace theorem for Dirichlet forms on fractals |
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Authors: | Masanori Hino Takashi Kumagai |
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Institution: | a Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan b Research Institute for Mathematical, Sciences, Kyoto University, Kyoto 606-8502, Japan |
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Abstract: | 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 Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field. |
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Keywords: | Trace theorem Self-similar sets Dirichlet forms Diffusions on fractals Lipschitz spaces Besov spaces Sierpinski carpets |
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