Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Huang, Genggeng"'
We study the regularity of the $p$-Gauss curvature flow with flat side. In our previous paper(arxiv:2403.12292), we obtained the regularity of the interface, namely the boundary of the flat part. In this paper, we study the regularity of the convex h
Externí odkaz:
http://arxiv.org/abs/2407.05663
Autor:
Hu, Dian, Huang, Genggeng
In this paper, we prove the a priori estimates for two-dimensional second order homogeneous linear elliptic equations in a narrow region. In a crescent-shaped area, part of the boundary is subject to an oblique derivative boundary condition, while th
Externí odkaz:
http://arxiv.org/abs/2407.03592
Autor:
Huang, Genggeng, Shen, Weiming
The Guillemin boundary condition naturally appears in the study of K\"ahler geometry of toric manifolds. In the present paper, the following Guillemin boundary value problem is investigated \begin{align} \label{eq1} &\det D^2 u=\frac{h(x)}{\prod_{i=1
Externí odkaz:
http://arxiv.org/abs/2406.05471
Autor:
Huang, Genggeng, Shen, Weiming
We study asymptotic behaviors of solutions to the Monge-Amp\`ere equation in cones and use the expansion as a tool to study the regularity of solutions in polygonal domains.
Externí odkaz:
http://arxiv.org/abs/2312.01405
We prove the existence of topological solutions to the self-dual Chern-Simons model and the Abelian Higgs system on the lattice graphs Z^n for n>1. This extends the results in Huang, Lin and Yau [HLY20] from finite graphs to lattice graphs.
Externí odkaz:
http://arxiv.org/abs/2310.13905
Autor:
Huang, Genggeng, Niu, Yating
In this paper, we classify the solutions of the following critical Choquard equation \[ (-\Delta)^{\frac{n}{2}} u(x) = \int_{\mathbb{R}^n} \frac{e^{\frac{2n- \mu}{2}u(y)}}{|x-y|^{\mu}}dy e^{\frac{2n- \mu}{2}u(x)}, \ \text{in} \ \mathbb{R}^n, \] where
Externí odkaz:
http://arxiv.org/abs/2310.08264
Autor:
Huang, Genggeng, Niu, Yating
In this paper, we classify the solution of the following mixed-order conformally invariant system with coupled nonlinearity in $ \mathbb{R}^4$: \begin{equation}\left\{ \begin{aligned} & -\Delta u(x) = u^{p_1}(x) e^{q_1v(x)}, \quad x\in \mathbb{R}^4,\
Externí odkaz:
http://arxiv.org/abs/2211.13881
In this paper, we prove the regularity of the free boundary in the Monge-Amp\`ere obstacle problem $\det D^2 v= f(y)\chi_{\{v>0\}}. $ By duality, the regularity of the free boundary is equivalent to that of the asymptotic cone of the solution to the
Externí odkaz:
http://arxiv.org/abs/2111.10575
Autor:
Huang, Genggeng, Lü, Yingshu
This paper is devoted to study the following degenerate Monge-Amp\`ere equation: \begin{eqnarray}\label{ab1} \begin{cases} \det D^2 u=\Lambda_q (-u)^q \quad \text{in}\quad \Omega,\\ u=0 \quad\text{on}\quad \partial\Omega \end{cases} \end{eqnarray} fo
Externí odkaz:
http://arxiv.org/abs/2012.02656
Autor:
Huang, Genggeng, Lü, Yingshu
Publikováno v:
In Journal of Differential Equations 15 December 2023 376:633-654