Lichun Liang

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20242026

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math.AP2026

Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides

Lichun Liang

In this paper, let $u \in C^{4} (B_{10})$ with $D^{2} u \geq - K I$ define a $2$ -admissible graph $M = {(x, u (x)) : x \in B_{10}} \subset R^{n + 1}$ satisfying \[ σ_2(κ[u])=f(x). \] We prove an int…

math.AP2026

Interior Hessian Estimates for Semi-convex Solutions of the $σ_{2} / σ_{1}$ Equation with Lipschitz Right-Hand Sides

Ke Ji, Lichun Liang

Let $n \geq 2$ and let $u$ be a smooth 2-convex and semi-convex solution of \[ \frac{σ_2(D^2u)}{σ_1(D^2u)}=f(x). \] We prove an interior Hessian estimate depending on the Lipschitz no…

math.AP2026

Liouville theorem for fully nonlinear elliptic equations with the small oscillation and the periodicity in $x$ and the periodic right hand term

Lichun Liang

In this paper, we study quadratic growth solutions $u$ of fully nonlinear elliptic equations of the form $F (D^{2} u, x) = f$ in $R^{n}$ , where $f$ is periodic and $F$ has the peri…

math.AP2026

The asymptotic behavior for divergence elliptic equations in exterior domains with periodic coefficients

Lichun Liang

In this paper, we investigate the asymptotic behavior of solutions for divergence linear elliptic equations in exterior domains with periodic coefficients. Consequently, we general…

Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides

Interior Hessian Estimates for Semi-convex Solutions of the σ2​/σ1​ Equation with Lipschitz Right-Hand Sides

Liouville theorem for fully nonlinear elliptic equations with the small oscillation and the periodicity in x and the periodic right hand term

The asymptotic behavior for divergence elliptic equations in exterior domains with periodic coefficients

Interior Hessian Estimates for Semi-convex Solutions of the $σ_{2} / σ_{1}$ Equation with Lipschitz Right-Hand Sides

Liouville theorem for fully nonlinear elliptic equations with the small oscillation and the periodicity in $x$ and the periodic right hand term