3 citations · 9 across the 18 of their papers we have counts for
18 papers
Higher Weak Differentiability to Mixed Local and Nonlocal Degenerate Elliptic Equations in the Heisenberg Group
Junli Zhang, Pengcheng Niu
In this paper, we investigate the higher weak differentiability of solutions to a class of mixed local and nonlocal degenerate elliptic equations in the Heisenberg group $\mathbb{H…
Regularity for Mixed Local and Nonlocal Degenerate Elliptic Equations in the Heisenberg Group
Junli Zhang, Pengcheng Niu
In this paper, we investigate the regularity for mixed local and nonlocal degenerate elliptic equations in the Heisenberg group. Inspired by the De Giorgi-Nash-Moser theory, the lo…
MiniMax-01: Scaling Foundation Models with Lightning Attention
MiniMax, Aonian Li, Bangwei Gong +87
We introduce MiniMax-01 series, including MiniMax-Text-01 and MiniMax-VL-01, which are comparable to top-tier models while offering superior capabilities in processing longer conte…
Notes on Liouville type Theorems for the stationary compressible Navier-Stokes equations
Zhouyu Li, Pengcheng Niu
In this paper, we investigate the three dimensional stationary compressible Navier-Stokes equations, and obtain Liouville type theorems if a smooth solution satis…
Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator
Pengyan Wang, Li Chen, Pengcheng Niu
In this paper, the positive solutions to Choquard equation involving fully nonlinear nonlocal operator are shown to be symmetric and monotone by using the moving plane method which…
On some Liouville type Theorems for the stationary MHD and Hall-MHD equations
Zhouyu Li, Pan Liu, Pengcheng Niu
We prove several Liouville type results for the stationary MHD and Hall-MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces…
On a Conjecture of Cai-Zhang-Shen for Figurate Primes
Junli Zhang, Pengcheng Niu
A conjecture of Cai-Zhang-Shen for figurate primes says that every integer is the sum of two figurate primes. In this paper we give an equivalent proposition to the conjectur…
Global well-posedness and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of the 2-D MHD equation
Zhouyu Li, Pan Liu, Pengcheng Niu
This paper is concerned with the Cauchy problem of the two-dimensional MHD system with magnetic diffusion. It was proved that the MHD equations have a unique global strong solution…
A Nash Type result for Divergence Parabolic Equation related to Hormander's vector fields
Lingling Hou, Pengcheng Niu
In this paper we consider the divergence parabolic equation with bounded and measurable coefficients related to Hormander's vector fields and establish a Nash type result, i.e., t…
A proof of Riemann Hypothesis
Pengcheng Niu, Junli Zhang
Let be a function relating to the Riemann zeta function with . In this paper, we construct a function containing and , and prove…
Some New Inequalities of Dirichlet Eigenvalues for Laplace Operator with any Order
Na Huang, Pengcheng Niu
In this paper, we establish several inequalities of Dirichlet eigenvalues for Laplace operator with any order on \emph{n}-dimensional Euclidean space. These inequalities are mo…
Higher gradients estimates in Morrey spaces for weak solutions to linear ultraparabolic equations
Yan Dong, Pengcheng Niu
The aim of this paper is to consider the linear ultraparabolic equation with bounded and VMO coefficients . Assume that the operator obtained by freezing the coef…
Regularity for weak solutions to nondiagonal quasilinear degenerate elliptic systems
Yan Dong, Pengcheng Niu
The aim of this paper is to establish regularity for weak solutions to the nondiagonal quasilinear degenerate elliptic systems related to Hörmander's vector fields, where the coeff…
Existence of optimizers of the Stein-Weiss inequalities on Carnot groups
Tingxi Hu, Pengcheng Niu
This paper proves existence of optimizers of the Stein-Weiss inequalities on Carnot groups under some conditions. The adjustment of Lions' concentration compactness principles to C…
Schauder estimates for solutions of sub-Laplace equations with Dini terms
Tingxi Hu, Pengcheng Niu
In this paper we establish Schauder estimates for the sublalpace equation \[Σ_{j = 1}^mX_j^2u = f,\] where is a system of smooth vector field which gen…
Hardy-Littlewood-Sobolev Type Inequality and Stein-Wiess Type Inequality on Carnot Groups
Tingxi Hu, Pengcheng Niu
A Stein-Weiss type inequality on Carnot groups is established by proving the boundedness of an integral operator and the Hardy-Littlewood-Sobolev type inequality on Carnot groups i…
Interior HW^{1,p} estimates for divergence degenerate elliptic systems in Carnot groups
Maochun Zhu, Marco Bramanti, Pengcheng Niu
Let X_1,...,X_q be the basis of the space of horizontal vector fields on a homogeneous Carnot group in R^n (q<n). We consider a degenerate elliptic system of N equations, in diverg…
Estimates in Generalized Morrey Spaces for Weak Solutions to Divergence Degenerate Parabolic Systems
Yan Dong, Maochun Zhu, Pengcheng Niu
Let be a family of real smooth vector fields satisfying Hömander's condition. The purpose of this paper is to establish gradient estimates in general…