38 citations · 49 across the 8 of their papers we have counts for
8 papers
A priori estimates for anti-symmetric solutions to a fractional Laplacian equation in a bounded domain
Chenkai Liu, Shaodong Wang, Ran Zhuo
In this paper, we obtain a priori estimates for the set of anti-symmetric solutions to a fractional Laplacian equation in a bounded domain using a blowing-up and rescaling argument…
A priori estimates for higher-order fractional Laplace equations
Yugao Ouyang, Meiqing Xu, Ran Zhuo
In this paper, we establish a priori estimates for the positive solutions to a higher-order fractional Laplace equation on a bounded domain by a blowing-up and rescaling argument.…
A localized criterion for the regularity of solutions to Navier-Stokes equations
Congming Li, Chenkai Liu, Ran Zhuo
The Serrin-Prodi-Ladyzhenskaya type criteria for the regularity of solutions to the incompressible Navier-Stokes equations are fundamental in the study of the millennium…
Qualitative properties of solutions for system involving fractional Laplacian
Ran Zhuo, Yingshu Lü
In this paper, we consider the following nonlinear system involving the fractional Laplacian \begin{equation} \left\{\begin{array}{ll} (-Δ)^{s} u (x)= f(u,\,v), \\ (-Δ)^{s} v (x)=…
On the Dirichlet problem for fractional Laplace equation on a general domain
Chenkai Liu, Ran Zhuo
In this paper, we study Dirichlet problems of fractional Laplace (Poisson) equations on a general bounded domain in . Green's functions and Poisson kernels are import…
The A Priori Estimate and Existence of the Positive Solution for A Nonlinear System Involving the Fractional Laplacian
Ran Zhuo, Yan Li
In the paper, we consider the fractional elliptic system \begin{equation*}\left\{\begin{array}{ll} (- Δ)^{\frac{α_1}{2}}u(x)+\sum\limits^n_{i=1}b_i(x)\frac{\partial u}{\partial x_i…
A Liouville Theorem for the Higher Order Fractional Laplacian
Ran Zhuo, Yan Li
We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differe…
A Liouville Theorem for the Fractional Laplacian
Ran Zhuo, Wenxiong Chen, Xuewei Cui +1
We extend the classical Liouville Theorem from Laplacian to the fractional Laplacian, that is, we prove Every -harmonic function bounded either above or below in all of mu…