1 citations · 1 across the 9 of their papers we have counts for
6 papers · 2 filters
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…