Lichun Liang

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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…

math.AP2025

A note on the Liouville theorem of fully nonlinear elliptic equations

Dongsheng Li, Lichun Liang

In this paper, a new method is presented to investigate the asymptotic behavior of solutions to the fully nonlinear uniformly elliptic equation $F (D^{2} u) = 0$ in exterior domains. Thi…

math.AP2025

Quadratic growth solutions of fully nonlinear elliptic equations with periodic data

Dongsheng Li, Lichun Liang

In this paper, we study quadratic growth solutions $u$ of fully nonlinear elliptic equations of the form $F (D^{2} u) = f$ in $R^{n}$ , where $f$ is periodic and $F$ may be not uni…

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

A note on the Liouville theorem of fully nonlinear elliptic equations

Quadratic growth solutions of fully nonlinear elliptic equations with periodic data

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