Hui Yang

Hong Kong University of Science and Technology

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Wenming Zou

Tsinghua University

Xusheng Du

Hong Kong University of Science and Technology

Tianling Jin

Hong Kong University of Science and Technology

Jing Cheng

China University of Petroleum, East China

Yao-Zhong Zhang

Northwestern Polytechnical University

Liming Ling

South China University of Technology

Yansheng Ma

Sichuan University

Changjia Wang

Changchun University of Science and Technology

Li-Min Wang

National Taiwan University

Beifang Chen

Guangdong University of Petrochemical Technology

Cooperative Institutions

Tsinghua University

Hong Kong University of Science and Technology

University of Hong Kong

Peng Cheng Laboratory

Beijing Normal University

Tongji University

Central China Normal University

South China University of Technology

Institute of Applied Physics and Computational Mathematics

Fujian Normal University

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On Pointed Hopf Algebras with Weyl Groups of exceptional type

arXiv (Cornell University) (2008)

Yao-Zhong Zhang Yao-Zhong Zhang Peng Wang Jing Cheng Hui Yang

All -1-type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non -1-type pointed Hopf algebra with real $G(H)$ is infinite dimensional and every central quantum linear space over finite group is finite dimensional. It is proved that except a few cases Nichols algebras of reducible Yetter-Drinfeld modules over Weyl groups of exceptional type are infinite dimensional.

10.48550/arxiv.0804.2602

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Citations (9)

A priori estimates versus arbitrarily large solutions for fractional semi-linear elliptic equations with critical Sobolev exponent

arXiv (Cornell University) (2021)

Xusheng Du Hui Yang

We study positive solutions to the fractional semi-linear elliptic equation $$ (- \Delta)^\sigma u = K(x) u^\frac{n + 2 \sigma}{n - 2 \sigma} ~~~~~~ in ~ B_2 \setminus \{ 0 \} $$ with an isolated singularity at the origin, where $K$ is a positive function on $B_2$, the punctured ball $B_2 \setminus \{ 0 \} \subset \mathbb{R}^n$ with $n \geq 2$, $\sigma \in (0, 1)$, and $(- \Delta)^\sigma$ is the fractional Laplacian. In lower dimensions, we show that, for any $K \in C^1 (B_2)$, a positive solution $u$ always satisfies that $u(x) \leq C |x|^{ - (n - 2 \sigma)/2 }$ near the origin. In contrast, we construct positive functions $K \in C^1 (B_2)$ in higher dimensions such that a positive solution $u$ could be arbitrarily large near the origin. In particular, these results also apply to the prescribed boundary mean curvature equations on $\mathbb{B}^{n+1}$.

Fractional Laplacian

Exponent

Sigma

Ball (mathematics)

10.48550/arxiv.2110.09048

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Local estimates for conformal $Q$-curvature equations

arXiv (Cornell University) (2021)

Tianling Jin Hui Yang

We derive local estimates of positive solutions to the conformal $Q$-curvature equation $$ (-\Delta)^m u = K(x) u^{\frac{n+2m}{n-2m}} ~~~~~~ in ~ \Omega \backslash \Lambda $$ near their singular set $\Lambda$, where $\Omega \subset \mathbb{R}^n$ is an open set, $K(x)$ is a positive continuous function on $\Omega$, $\Lambda$ is a closed subset of $\mathbb{R}^n$, $2 \leq m < n/2$ and $m$ is an integer. Under certain flatness conditions at critical points of $K$ on $\Lambda$, we prove that $u(x) \leq C [{dist}(x, \Lambda)]^{-(n-2m)/2}$ when the upper Minkowski dimension of $\Lambda$ is less than $(n-2m)/2$.

Flatness (cosmology)

10.48550/arxiv.2107.04437

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Citations (1)

Stable and finite Morse index solutions of a nonlinear elliptic system

Journal of Mathematical Analysis and Applications (2018)

Hui Yang Wenming Zou

Exponent

Matrix (chemical analysis)

10.1016/j.jmaa.2018.10.069

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Citations (3)

Existence of Solutions to a Conformally Invariant Integral Equation Involving Poisson-Type Kernels

Journal of Geometric Analysis (2023)

Xusheng Du Tianling Jin Hui Yang

Antipodal point

Poisson's equation

Poisson kernel

10.1007/s12220-023-01350-6

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Attractors and Inertial Manifolds

De Gruyter eBooks (2018)

Boling Guo Liming Ling Yansheng Ma Hui Yang

This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold

10.1515/9783110549652

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Citations (1)

Qualitative analysis for an elliptic system in the punctured space

Zeitschrift für angewandte Mathematik und Physik (2020)

Hui Yang Wenming Zou

Component (thermodynamics)

Backslash

BETA (programming language)

10.1007/s00033-020-1270-4

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Citations (1)

Qualitative analysis for an elliptic system in the punctured space

arXiv (Cornell University) (2018)

Hui Yang Wenming Zou

In this paper, we investigate the qualitative properties of positive solutions for the following two-coupled elliptic system in the punctured space: $$ \begin{cases} -\Delta u =\mu_1 u^{2q+1} + \beta u^q v^{q+1} \\ -\Delta v =\mu_2 v^{2q+1} + \beta v^q u^{q+1} \end{cases} \textmd{in} ~\mathbb{R}^n \backslash \{0\}, $$ where $\mu_1, \mu_2$ and $\beta$ are all positive constants, $n\geq 3$. We establish a monotonicity formula that completely characterizes the singularity of positive solutions. We prove a sharp global estimate for both components of positive solutions. We also prove the nonexistence of positive semi-singular solutions, which means that one component is bounded near the singularity and the other component is unbounded near the singularity.

Backslash

BETA (programming language)

Component (thermodynamics)

Qualitative analysis

Isolated singularity

10.48550/arxiv.1811.07079

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Super Polyharmonic Property and Asymptotic Behavior of Solutions to the Higher Order Hardy-Henon Equation Near Isolated Singularities

Xia Huang Yuan Li Hui Yang

In this paper, we are devoted to studying the positive solutions of the following higher order Hardy-H\'enon equation[[EQUATION]]with an isolated singularity at the origin, where $n > 2m$, $\alpha > -2m$ and $m\geq1$ is an integer. For $1 < p < \frac{n+2m}{n-2m}$, we prove the singularity and decay estimates of solutions. For $\frac{n+\alpha}{n-2m} < p < \frac{n+2m}{n-2m}$ with $-2m<\alpha<2m$, we show the super polyharmonic properties of solutions near the singularity, which are essential in studying polyharmonic equations. By utilizing these properties, we classify the isolated singularities and establish the precise asymptotic behavior of solutions for the fourth order case. Furthermore, we also classify the isolated singularities at infinity and show a uniqueness theorem for the fourth order Lane-Emden equation.

10.2139/ssrn.4498197

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Citations (1)

Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem

arXiv (Cornell University) (2021)

Xusheng Du Tianling Jin Jingang Xiong Hui Yang

We show a convergence result of the fractional Laplacian for sequences of nonnegative functions without uniform boundedness near infinity. As an application, we construct a sequence of solutions to the fractional Nirenberg problem that blows up in the region where the prescribed functions are negative. This is a different phenomenon from the classical Nirenberg problem.

Fractional Laplacian

Infinity

Sequence (biology)

10.48550/arxiv.2112.00960

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