76 citations · 227 across the 25 of their papers we have counts for
25 papers
Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions
Chang-Yu Guo, Changyou Wang, Chang-Lin Xiang
Energy identity for harmonic type maps in supercritical dimensions is an important and difficult problem. For sphere-valued harmonic maps, the first breakthrough was achieved by Li…
Quantitative regularity for minimizing intrinsic fractional harmonic maps
Y. -Y. Wang, C. -L. Xiang, G. -F. Zheng
In this note, we study compactness and regularity theory of minimizing intrinsic fractional harmonic mappings introduced by Moser and Roberts. Based on the partial regularity theor…
Conservation law of harmonic mappings in supercritical dimensions
Chang-Yu Guo, Chang-Lin Xiang
In this short note, we provide a partial extension of Rivière's convervation law in higher dimensions under certain Lorentz integrability condition for the connection matrix. As an…
Sharp Morrey regularity theory for a fourth order geometrical equation
Chang-Lin Xiang, Gao-Feng Zheng
This paper is a continuation of the recent work of Guo-Xiang-Zheng \cite{Guo-Xiang-Zheng-2021-CV}. We deduce sharp Morrey regularity theory for weak solutions to the fourth order n…
The conservation law approach in geometric PDEs
Chang-Yu Guo, Chang-Lin Xiang
In this survey paper, we give an overview of the conservation law approach in the study of geometric PDEs that models in particular polyharmonic maps.
Global conservation law for an even order elliptic system with antisymmetric potential
Chang-Yu Guo, Chang-Lin Xiang, Gao-Feng Zheng
In this note, we refine the local conservation law obtained by Lamm-Rivière for fourth order systems and de Longueville-Gastel for general even order systems to a global conservati…
regularity theory for even order elliptic systems with antisymmetric first order potentials
Chang-Yu Guo, Chang-Lin Xiang, Gao-Feng Zheng
Motivated by a challenging expectation of Rivière (2011), in the recent interesting work of deLongueville-Gastel (2019), de Longueville and Gastel proposed the following geometrica…
Regularity of weak solutions to higher order elliptic systems in critical dimensions
Chang-Yu Guo, Chang-Lin Xiang
In this paper, we develop an elementary and unified treatment, in the spirit of Rivière and Struwe (Comm. Pure. Appl. Math. 2008), to explore regularity of weak solutions of higher…
The Lamm-Riviere system I: regularity theory
Chang-Yu Guo, Chang-Lin Xiang, Gao-Feng Zheng
Motived by the heat flow and bubble analysis of biharmonic mappings, we study further regularity issues of the fourth order Lamm-Riviere system $$Δ^{2}u=Δ(V\cdot\nabla u)+{\rm div}…
Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth
Gongbao Li, Chang-Lin Xiang
In this paper, we prove uniqueness and nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3…
Some regularity results for -harmonic mappings between Riemannian manifolds
Chang-Yu Guo, Chang-Lin Xiang
Let be a -smooth Riemannian manifold with boundary and a complete -smooth Riemannian manifold. We show that each stationary -harmonic mapping ,…
Regularity of quasi-n-harmonic mappings into NPC spaces
Chang-Yu Guo, Chang-Lin Xiang
We prove local Holder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain globa…
Multi-peak positive solutions to a class of Kirchhoff equations
Peng Luo, Shuangjie Peng, Chunhua Wang +1
In the present paper, we consider the nonlocal Kirchhoff problem \begin{eqnarray*} -\left(ε^2a+εb\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)Δu+V(x)u=u^{p},\,\,\,u>0 & & \text{in }\m…
Uniqueness and Nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems
Gongbao Li, Peng Luo, Shuangjie Peng +2
In the present paper, we establish the uniqueness and nondegeneracy of positive energy solutions to the Kirchhoff equation \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla…
Uniqueness and nondegeneracy of positive solutions to a class of Kirchhoff equations in
Gongbao Li, Shuangjie Peng, Chang-Lin Xiang
In this paper, we establish a type of uniqueness and nondegeneracy results for positive solutions to the following nonlocal Kirchhoff equations \begin{eqnarray*} -\left(a+b\int_{\m…
Nonlinear Liouville problems in a quarter plane
Chang-Lin Xiang
We answer affirmatively the open problem proposed by Cabré and Tan in their paper "Positive solutions of nonlinear problems involving the square root of the Laplacian" (see Adv. Ma…
-variational problems associated to measurable Finsler structures
Chang-Yu Guo, Chang-Lin Xiang, Dachun Yang
We study -variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.
Remarks on Nondegeneracy of Ground States for Quasilinear Schrödinger Equations
Chang-Lin Xiang
In this paper, we answer affirmatively the problem proposed by A. Selvitella in his paper "Nondegenracy of the ground state for quasilinear Schrödinger Equations" (see Calc. Var. P…
Uniqueness and Nondegeneracy of Ground States for Choquard Equations in three dimensions
Chang-Lin Xiang
We obtain uniqueness and nondegeneracy results for ground states of Choquard equations in , provided that a…
Uniqueness of Positive Radial Solutions To Singular Critical Growth Quasilinear Elliptic Equations
Cheng-Jun He, Chang-Lin Xiang
In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth \[ \begin{cases} -Δ…
Gradient Estimates for Solutions To Quasilinear Elliptic Equations with Critical Sobolev Growth and Hardy Potential
Chang-Lin Xiang
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -Δ_{p}u-\fracμ{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2…
Asymptotic Behaviors of Solutions to quasilinear elliptic Equations with critical Sobolev growth and Hardy potential
Chang-Lin Xiang
Optimal estimates on the asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \[-Δ_{p}u-\fracμ…
Quantitative Properties on the Steady States to A Schrödinger-Poisson-Slater System
Changlin Xiang
A relatively complete picture on the steady states of the following Schrdinger-Poisson-Slater (SPS) system \[ \begin{cases} -ΔQ+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R…
Liouville Type Theorem For A Nonlinear Neumann Problem
Changlin Xiang
Consider the following nonlinear Neumann problem \[ \begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a…