4 citations · 6 across the 7 of their papers we have counts for
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A Sierpinski carpet like fractal without standard self-similar energy
Shiping Cao, Hua Qiu
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 ex…
Convergence of energy forms on Sierpinski gaskets with added rotated triangle
Shiping Cao
We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dir…
Existence and uniqueness of diffusions on the Julia sets of Misiurewicz-Sierpinski maps
Shiping Cao, Malte S. Hassler, Hua Qiu +2
We study the balanced resistance forms on the Julia sets of Misiurewicz-Sierpinski maps, which are self-similar resistance forms with equal weights. In particular, we use a theorem…
Sobolev spaces on p.c.f. self-similar sets: boundary behavior and interpolation theorems
Shiping Cao, Hua Qiu
We study the Sobolev spaces and on p.c.f. self-similar sets in terms of the boundary behavior of functions. First, for , we make an exact des…
Sobolev spaces on p.c.f. self-similar sets: critical orders and atomic decompositions
Shiping Cao, Hua Qiu
We consider the Sobolev type spaces with , where is a post-critically finite self-similar set with the natural boundary. Firstly, we compare different classes…
Sobolev spaces and trace theorem on the Sierpinski gasket
Shiping Cao, Hua Qiu
On the Sierpinski gasket , we consider Sobolev spaces associated with the standard Laplacian with order . When ,…