Author

Kai Sheng

2 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

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 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