Jin Yan

activity

20242026

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8 papers · 1 filter

math.AP2026

Boundary regularity of $k$ -Hessian eigenfunctions

Guohuan Qiu, Jin Yan

We prove smoothness up to the boundary for $k$ -Hessian eigenfunctions on smooth bounded uniformly convex domains when $2 \leq k < n$ . This resolves an open problem in the regularity t…

math.AP2026

Sharp Hessian integrability for the planar Monge--Ampère equation

XiaoRui Lu, Jin Yan, Bao Yu +1

We determine the optimal local integrability of the Hessian for planar convex Alexandrov solutions satisfying $λ d x \leq μ_{u} \leq λ^{- 1} d x, 0 < λ < 1.$ The distributional Hes…

math.AP2026

Ground states of a logarithmic Schrödinger equation with a power perturbation in $R^{N}$ : existence, uniqueness and nondegeneracy

Jinqi Yan, Bo You

The objective of this paper is to study the existence and uniqueness of positive ground state solutions of the following Schrödinger problem \[ -Δu=u\log u^2+μ\abs{u}^{p-1}u\qquad\…

math.AP2026

The $m$ -Laplace equation with a gradient term II: classification in the second critical case

Tian Wu, Jin Yan, Hua Zhu

Let $1 < m < n$ and $0 < q < m - 1$ . We classify positive, locally bounded weak solutions of \[-Δ_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\righ…

math.AP2026

Interior estimates for Hessian quotient equations

Guohuan Qiu, Jin Yan

We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator…

math.AP2026

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

Guohuan Qiu, Jin Yan

We resolve the long-standing problem of establishing interior $C^2$ estimates for admissible solutions of the graphical scalar curvature equation in every dimension $n\ge 3$. M…

math.DG2026

The asymptotic Plateau problem for Hypersurfaces of constant $H_{k}$ curvature in hyperbolic space

Xinqun Mei, Jin Yan

In this paper, we study the asymptotic Plateau problem in hyperbolic space for hypersurfaces of constant $H_{k}$ -curvature. We prove the existence of a smooth complete $k$ -convex hyp…

math.AP2026

Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions

Xinqun Mei, Jin Yan

In this paper, we study the interior $C^{2}$ estimates for Hessian quotient equations $\frac{σ _{3} ( D ^{2} u )}{σ _{l} ( D ^{2} u )} = 1$ for $l = 1, 2$ , in arbitrary dimensions, under the natur…

Boundary regularity of k-Hessian eigenfunctions

Sharp Hessian integrability for the planar Monge--Ampère equation

Ground states of a logarithmic Schrödinger equation with a power perturbation in RN: existence, uniqueness and nondegeneracy

The m-Laplace equation with a gradient term II: classification in the second critical case

Interior estimates for Hessian quotient equations

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

The asymptotic Plateau problem for Hypersurfaces of constant Hk​ curvature in hyperbolic space

Interior C2 estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions

Boundary regularity of $k$ -Hessian eigenfunctions

Ground states of a logarithmic Schrödinger equation with a power perturbation in $R^{N}$ : existence, uniqueness and nondegeneracy

The $m$ -Laplace equation with a gradient term II: classification in the second critical case

The asymptotic Plateau problem for Hypersurfaces of constant $H_{k}$ curvature in hyperbolic space

Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions