Author

Jia-Huan Li

h-index 2 View on Semantic Scholar

We have 6 of 12 papers

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

Isolated singularities of the capillary equation with negative gravity

We classify isolated singularities of classical solutions to the capillary equation with negative gravity, \[ \operatorname{div}\frac{Du}{\sqrt{1+|Du|^2}}=-u \qquad\text{in }B_R\setminus\{0\}\subset\mathbb R^n, \qquad n\ge2, \] without a priori assumptions on symmetry, sign, one-sided boundedness, or blow-up rate. Ever...

Bing Deng, Jia-Huan Li, Yi-Lu Liu et al. · 0 citations

Preprint Aug 2026

A Brunn--Minkowski inequality and Convexity for the 2-Hessian eigenvalue in convex domains

We prove the strict log-concavity of the positive first eigenfunction $-u$ of the $2$-Hessian equation and the strict $1/2$-convexity of the solution for the corresponding torsion problem in smooth bounded uniformly convex domains in $\mathbb{R}^{n}$. As applications, we establish the associated Brunn--Minkowski in...

Jia-Huan Li, Xi-Nan Ma, Guo-Huan Qiu et al. · 1 citation · ⚡1

Preprint Aug 2026

A Local Lewy Theorem for $p$-Harmonic Function with Non-zero Gradient in $R^3$

We establish a local Lewy-type theorem for $p$-harmonic function with non-zero gradient in dimension three space $R^3$. Let $1<p<\infty$, and let $u\in W^{1,p}_{\mathrm{loc}}(\Omega)$ be a weak $p$-harmonic function in a domain $\Omega\subset\mathbb R^3$, assume it satisfies $|Du|>0$, we prove that a locall...

Jia-Huan Li, Yi-Lu Liu, Xi-Nan Ma · 2 citations · ⚡1

Preprint Aug 2026

The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity

Let $n\ge3$ and let $h:\A(r,1)\to\A(R,1)\subset\mathbb R^n$ be an onto homeomorphism with harmonic coordinate functions. We prove the sharp Nitsche bound \[ R\le R_{n,+}(r):=\frac{nr}{n-1+r^n}, \] and, when $h$ interchanges the two ends, the strictly stronger sharp bound \[ R\le R_{n,-}(r):=\frac{nr^{n-1}}{1+(n-1)r^n}....

Bing Deng, Jia-Huan Li, Yi-Lu Liu et al. · 0 citations

Preprint Jul 2026

Strict Convexity for Solution of Liouville-Type Dirichlet Problems

We identify a common convexity structure for three exponential Dirichlet problems on smooth uniformly strictly convex domains: the Liouville equation $\Delta u=e^u$, the real equation $\sigma_2(D^2u)=e^{2u}$, and its complex counterpart $\sigma_2(u_{i\bar j})=e^{2u}$. In each case $u<0$ in the domain and $u=0$ on the b...

Jiahuan Li, Shuning Xu · 0 citations

Preprint Aug 2026

Strict Concavity of the Torsion Function for the Restricted Half-Laplacian in Bounded Convex Domains

Let $D\subset\mathbb{R}^n$, $n\ge2$, be a bounded convex domain, and let $u_D$ be the torsion function for the restricted half-Laplacian. We prove that $D^2u_D$ is negative definite at every point of $D$. The argument is based on the reflected harmonic extension in a slit domain. Quantitative Schauder estimates in slit...

Jia-Huan Li, Shu-Jun Shi · 0 citations