3 papers
math.AP2025
State-Constrained Chemical Reactions: Discrete-to-Continuous Hamilton--Jacobi Equations and Large Deviations
Yuan Gao, Yuxi Han
We study the macroscopic behavior of chemical reactions modeled as random time-changed Poisson processes on discrete state spaces. Using the WKB reformulation, the backward equatio…
math.AP2024
Carleman estimates for higher order partial differential operators and its applications
Xiaoyu Fu, Yuan Gao
In this paper, we obtain a Carleman estimate for the higher order partial differential operator. In the process of establishing this estimate, we developed a new method, which is c…
math.AP2023
Double-tower Solutions for Higher Order Prescribed Curvature Problem
Yuan Gao, Yuxia Guo, Yichen Hu
We consider the following higher order prescribed curvature problem on \begin{equation*} D^m \tilde u=\widetilde{K}(y) \tilde u^{m^{*}-1} \quad \mbox{on} \ {\m…