A Sierpinski carpet like fractal without standard self-similar energy

Published 27 Sep 2021 in math.FA and math.PR | (2109.12760v1)

Abstract: We construct a Sierpinski carpet like fractal, on which a self-similar diffusion with sub-Gaussian heat kernel estimate does not exist, in contrast to previous researches on the existence of such diffusions, on the generalized Sierpinski carpets and recently introduced unconstrained Sierpinski carpets.

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