arXiv subjects

Yating Niu

Publications and source records attributed to Yating Niu.

4 recordsLinked to original sources

arXiv2026

A sharp curvature lower bound for the first exterior p-harmonic Steklov eigenvalue

In this paper, we study the first variational Steklov eigenvalue of the $ p$-Laplace equation on exterior domain $ \Omega^{\text{ext}}$ for $ 1< p <n$. If $ \Omega$ is convex and $ \partial \Omega\in C^{1,1}$, we prove a sharp lower bound in terms of $p$-logarithmic mean of the principal curvatures of $ \partial \Omega$. For the linear case $ p=2$, our estimate reduces to the logarithmic mean bound of Bundrock et al. (arXiv:2511.09490). We also derive an upper bound in terms of a boundary isocapacitary constant. The analysis relies on the established finite energy theory on exterior domains, together with a decay estimate for $p$-harmonic extensions.

math.AP↗

arXiv2023

Classification of solutions of higher order critical Choquard equation

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 $ 0<\mu < n$, $ n\ge 2$. Suppose $ u(x) = o(|x|^2) \ \text{at} \ \infty $ for $ n \geq 3$ and satisfies \[ \int_{\mathbb{R}^n}e^{\frac{2n- \mu}{2}u(y)} dy < \infty, \ \int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{e^{\frac{2n- \mu}{2}u(y)}}{|x-y|^{\mu}} e^{\frac{2n- \mu}{2}u(x)} dy dx < \infty. \] By using the method of moving spheres, we show that the solutions have the following form \[ u(x)= \ln \frac{C_1(\varepsilon)}{|x-x_0|^2 + \varepsilon^2}. \]

math.AP↗

arXiv2022

Classification of solutions for some mixed order elliptic system

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,\\ & (-\Delta)^2 v(x) = u^{p_2}(x) e^{q_2v(x)}, \quad x\in \mathbb{R}^4, \end{aligned} \right. \end{equation} where $ 0\leq p_1 < 1$, $ p_2 >0$, $ q_1 > 0$, $ q_2 \geq 0$, $ u>0$ and satisfies $$ \int_{\mathbb{R}^4} u^{p_1}(x) e^{q_1v(x)} dx < \infty,\quad \int_{\mathbb{R}^4} u^{p_2}(x) e^{q_2 v(x)} dx < \infty.$$ Under additional assumptions (H1) or (H2), we study the asymptotic behavior of the solutions to the system and we establish the equivalent integral formula for the system. By using the method of moving spheres, we obtain the classification results of the solutions in the system.

math.AP↗

arXiv2021

Liouville type theorem of integral equation with anisotropic struture

In this paper, we classify all positive solutions for the following integral equation: \begin{equation} u(x)=\int_{\mathbb{R}^n_+}K_b(x,y)y_n^b f(u(y))dy, \end{equation} where $ b > 1$ is a constant. Here $ K_b(x,y)$ is the Green function of the following homogeneous Neumann boundary problem \begin{equation} \left\{ \begin{aligned} -\text{div}(x^{b}_n \nabla u)&= f \quad in \mathbb{R}^n_+ \\ \frac{\partial u}{\partial x_n}&= 0 \quad on \ \partial \mathbb{R}^n_+ . \end{aligned} \right. \end{equation} By using the method of moving planes in integral form, we derive the symmetry of positive solutions. We also establish the equivalence between the integral equation and its corresponding partial differential equation. Similarly, the results can be generalized to the integral system.

math.AP↗