7 papers
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: $$ -Îu+(-Î)^s u=u^q\quad\text{in }\mathbb…
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} -Îu=f(X)\cdot u^{-γ} \end{equation} in a bounded Lipschitz domain , with the Dirichlet boundary condition an…
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} (-Î)^s…
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: $$ (\partial_t -Î)^{s} u(x,t) = f(x,t)\ \ \mbox{in}\ \mathbb{R}^n\times\mathbb{R} , $$ wh…