1 citations · 1 across the 9 of their papers we have counts for
11 papers · 1 filter
isomorphisms for the fractional Laplacian on and their application
Congming Li, Yugao Ouyang, Zixuan Wang
A classical theory of Amrouche, Girault and Giroire (1994) resolves the Laplace equation on through an isomorphism between weighted Sobolev spaces. Inspired by their…
Asymptotic Expansions of the Fundamental Solution for a Mixed Local-Nonlocal Operator
Congming Li, Ling Wang, Jiongduo Xie
In this paper, we study the fundamental solution of the mixed local-nonlocal operator We derive precise asymptotic expansions of the fundamental solution a…
Classification of global solutions to the singular equation in a Lipschitz epigraphical cone
Yahong Guo, Congming Li, Chilin Zhang
We construct and classify all global solutions to the singular equation supported in a general Lipschitz epigraphical cone, where is a locally Dini…
Liouville Theorems for the Lane-Emden Equation Involving a Mixed Local-Nonlocal Operator
Yahong Guo, Congming Li, Jiongduo Xie
In this paper, we investigate the existence of positive supersolutions for the following mixed local-nonlocal Lane-Emden type equation: $$ -Δu+(-Δ)^s u=u^q\quad\text{in }\mathbb R^…
A convergence result for the master operator
Wenxiong Chen, Yahong Guo, Congming Li +1
In this paper, we establish a convergence result for the fully fractional heat operator $\ma{s}$, also known as the master operator, stated as follows: \[\mbox{If\ }u_i\to u\ \mbox…
Methods in studying qualitative properties of fractional equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional equations. Beginning with the pioneering ex…
Boundary regularity and a priori estimates for fractional equations on unbounded domains
Yahong Guo, Congming Li, Yugao Ouyang
In this paper, we study the boundary Hölder regularity for solutions to the fractional Dirichlet problem in unbounded domains with boundary \begin{equation*} \begin{cases} (-Δ)^s u…
Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain
Yahong Guo, Congming Li, Chilin Zhang
We study the singular Lane-Emden-Fowler equation \begin{equation} -Δu=f(X)\cdot u^{-γ} \end{equation} in a bounded Lipschitz domain , with the Dirichlet boundary condition and a…
Refined regularity for nonlocal elliptic equations and applications
Wenxiong Chen, Congming Li, Leyun Wu +1
In this paper, we establish refined regularity estimates for nonnegative solutions to the fractional Poisson equation Specifically, we hav…
Regularity of solutions for fully fractional parabolic equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we study the fully fractional heat equation involving the master operator: $$ (\partial_t -Δ)^{s} u(x,t) = f(x,t)\ \ \mbox{in}\ \mathbb{R}^n\times\mathbb{R} , $$ whe…
The direct moving sphere for fractional Laplace equation
Congming Li, Meiqing Xu, Hui Yang +1
This paper works on the direct method of moving spheres and establishes a Liouville-type theorem for the fractional elliptic equation \[ (-Δ)^{α/2} u =f(u) ~~~~~~ \text{in } \mathb…