6 citations · 26 across the 15 of their papers we have counts for
4 papers · 1 filter
Sobolev inequalities on product Sierpinski spaces
Xuan Liu, Zhongmin Qian
On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions. Singularity of measures brings difficulties in (es…
A uniform approach to soliton cellular automata using rigged configurations
Xuan Liu, Travis Scrimshaw
For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a n…
Parabolic type equations associated with the Dirichlet form on the Sierpinski gasket
Xuan Liu, Zhongmin Qian
By using the analytic tools of Dirichlet forms, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along a frac…
A stochastic Pontryagin maximum principle on the Sierpinski gasket
Xuan Liu
In this paper, we consider stochastic control problems on the Sierpinski gasket. An order comparison lemma is derived using heat kernel estimate for Brownian motion on the gasket.…