Author

Chao Ji

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Preprint Sep 2026

Sharp Born--Infeld Sobolev inequality and extremal functions on the lattice graph $\mathbb Z^N$

In this paper, we study the sharp Sobolev-type inequality associated with the Born--Infeld energy on the lattice graph $\mathbb Z^N$, $N\geq3$: \[ \frac12\sum_{x\in\mathbb Z^N}\sum_{y\sim x} \left(1-\sqrt{1-|\nabla_{xy}u|^2}\right) \geq C_{N,\alpha} \left(\sum_{x\in\mathbb Z^N}|u(x)|^\alpha\right)^{\frac{N}{N+\alph...

Chao Ji, Kai Sheng · 0 citations

Preprint Sep 2026

Normalized solutions of $L^2$-supercritical NLS equations with periodic potentials

In this paper, we study normalized solutions to the following $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a periodic potential \begin{equation*} \begin{dcases} -\Delta u +V (x)u + \lambda u=\chi_{{\Omega}}(x)f(u)\quad \text{in } \mathbb{R}^N, u>0 \quad \text{in} \ \mathbb{R}^N, \int_{\mathbb{R}^N}\abs{u...

Zhen-Tao He, N. Ikoma, Chao Ji · 0 citations

Preprint Aug 2026

A partial answer to Brezis'Open Problem 2.1

In this paper, we give a partial answer to Brezis'Open Problem~2.1, which concerns the uniqueness of solutions to the Ginzburg--Landau equation in the unit disc with the degree-one boundary condition. Let $\lambda_1$ be the first Dirichlet eigenvalue of $-\Delta$ in the unit disc and set $\varepsilon_*:=\lambda_1^{-1/2...

Chao Ji, Kai Sheng · 0 citations