Locally symmetric polygon-based self-similar sets are shown to be p-conductively homogeneous for all p above their conformal dimension, yielding Sobolev spaces and diffusions even when the fractal has trivial isometry group.
Haj lasz,Sobolev spaces on an arbitrary metric spaces, Pontential Anal- ysis5(1996), 403–415
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Conductive homogeneity of locally symmetric polygon-based self-similar sets
Locally symmetric polygon-based self-similar sets are shown to be p-conductively homogeneous for all p above their conformal dimension, yielding Sobolev spaces and diffusions even when the fractal has trivial isometry group.