4 citations · 6 across the 7 of their papers we have counts for
11 papers
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…
A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket
Shiping Cao, Shuangping Li, Robert S. Strichartz +1
We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special…
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…