19 citations · 81 across the 40 of their papers we have counts for
6 papers · 1 filter
The fundamental gap of a kind of two dimensional sub-elliptic operator
Hongli Sun, Donghui Yang, Xu Zhang
This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak soluti…
Isospectral operators
Mu-Fa Chen, Xu Zhang
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of -transform (du…
The Theory of Stochastic Pseudo-differential Operators and Its Applications, I
Xu Liu, Xu Zhang
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we i…
Weak Maximum Principle for Strongly Coupled Elliptic Differential Systems
Xu Liu, Xu Zhang
A classical counterexample due to E. De Giorgi, shows that the weak maximum principle does not remain true for general linear elliptic differential systems. After that, there are s…
Carleman and Observability Estimates for Stochastic Wave Equations
Xu Zhang
Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equ…
Unique Continuation for Stochastic Parabolic Equations
Xu Zhang
This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classic…