46 citations · 191 across the 47 of their papers we have counts for
10 papers · 1 filter
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…
Spectral analysis beyond on Sierpinski lattices
Shiping Cao, Yiqi Huang, Hua Qiu +2
We study the spectrum of the Laplacian on the Sierpinski lattices. First, we show that the spectrum of the Laplacian, as a subset of , remains the same for any …
Analysis on hybrid fractals
Patricia Alonso Ruiz, Yuming Chen, Haotian Gu +2
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in…
Using Peano Curves to Construct Laplacians on Fractals
Denali Molitor, Nadia Ott, Robert Strichartz
We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia…
Boundary Value Problems for a Family of Domains in the Sierpinski Gasket
Zijian Guo, Hua Qiu, Robert S. Strichartz
For a family of domains in the Sierpinski gasket, we study harmonic functions of finite energy, characterizing them in terms of their boundary values, and study their normal deriva…
"Graph Paper" Trace Characterizations of Functions of Finite Energy
Robert S. Strichartz
We characterize functions of finite energy in the plane in terms of their traces on the lines that make up "graph paper" with squares of side length for all , and certain $…