Yuanyuan Lian

activity

20182026

most citedBoundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations

10 citations · 20 across the 19 of their papers we have counts for

collaborators

20 papers

math.DG2026

Asymptotic behavior at infinity of Weingarten surfaces

Aires E. M. Barbieri, José A. Gálvez, Yuanyuan Lian +1

We derive the asymptotic expansion at infinity for embedded ends of uniformly elliptic Weingarten surfaces with finite total curvature in $R^{3}$ , and we establish a maximum…

math.AP2026

Interior $B M O$ regularity for elliptic equations in divergence form

Yuanyuan Lian

In this note, we establish the interior $B M O$ regularity of weak solutions to uniformly elliptic equations in divergence form. Moreover, the assumptions on the coefficients are nea…

math.AP2025

Boundary Hölder gradient estimates for parabolic $p$ -Laplace type equations

Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1

In this paper, we study the boundary regularity for viscosity solutions of parabolic $p$ -Laplace type equations. In particular, we obtain the boundary pointwise $C^{1, α}$ regularit…

math.AP2025

Time derivative estimates for parabolic $p$ -Laplace equations and applications to optimal regularity

Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun +1

We establish the boundedness of time derivatives of solutions to parabolic $p$ -Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximat…

math.AP2024

Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets

Yuanyuan Lian

In this paper, we obtain the interior pointwise $C^{k, α}$ ( $k \geq 0$ , $0 < α < 1$ ) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness…

math.AP2024

Pointwise regularity for locally uniformly elliptic equations and applications

Yuanyuan Lian, Kai Zhang

In this paper, we study the regularity for viscosity solutions of locally uniformly elliptic equations and obtain a series of interior pointwise $C^{k, α}$ ( $k \geq 1$ , $0 < α < 1$ ) regu…

math.AP2024

Interior pointwise $C^{α}$ regularity for elliptic and parabolic equations with divergence-free drifts

Yuanyuan Lian

We investigate the interior pointwise $C^{α}$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability con…

math.AP2024

Asymptotic behavior for fully nonlinear elliptic equations in exterior domains

Lian Yuanyuan, Zhang Kai

In this paper, we obtain the asymptotic behavior at infinity for viscosity solutions of fully nonlinear elliptic equations in exterior domains. We show that if the solution $u$ gro…

math.AP2022★ 2 cited

Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries

Yuanyuan Lian, Kai Zhang

In this paper, we prove boundary pointwise $C^{k, α}$ regularity for any $k \geq 1$ for fully nonlinear parabolic equations. As an application, we give a direct and short proof of th…

math.AP2022★ 1 cited

Boundary pointwise regularity and Liouville theorems for fully nonlinear equations on cones

Yuanyuan Lian

In this paper, we prove a boundary pointwise regularity for fully nonlinear elliptic equations on cones. In addition, based on this regularity, we give simple proofs of the Liouvil…

math.AP2022

A note on the BMO and Calderón-Zygmund estimate

Yuanyuan Lian, Kai Zhang

In this note, we give a simple proof of the pointwise BMO estimate for Poisson's equation. Then the Calderón-Zygmund estimate follows by the interpolation and duality.

math.AP2022

Boundary pointwise regularity and applications to the regularity of free boundaries

Yuanyuan Lian, Kai Zhang

In this paper, we develop a series of boundary pointwise regularity for Dirichlet problems and oblique derivative problems. As applications, we give direct and simple proofs of the…

math.AP2021

Pointwise Boundary Differentiability for Fully Nonlinear Elliptic Equations

Duan Wu, Yuanyuan Lian, Kai Zhang

In this paper, we prove the pointwise boundary differentiability for viscosity solutions of fully nonlinear elliptic equations. This generalizes the previous related results for li…

math.AP2020★ 7 cited

Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms

Yuanyuan Lian, Lihe Wang, Kai Zhang

In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms. In particular, the equations with…

math.AP2019

Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations

Yuanyuan Lian, Wenxiu Xu, Kai Zhang

In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the dom…

math.NT2019

A simple proof of the transcendence of the trigonometric functions

Yuanyuan Lian, Kai Zhang

In this note, we give a simple proof that the values of the trigonometric functions at any nonzero rational number are transcendental numbers.

math.AP2019

On the boundary Hölder regularity for the infinity Laplace equation

Leyun Wu, Yuanyuan Lian, Kai Zhang

In this note, we prove the boundary Hölder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exter…

math.AP2019

Boundary Pointwise $C^{1, α}$ and $C^{2, α}$ Regularity for Fully Nonlinear Elliptic Equations

Yuanyuan Lian, Kai Zhang

In this paper, we obtain the boundary pointwise $C^{1, α}$ and $C^{2, α}$ regularity for viscosity solutions of fully nonlinear elliptic equations. I.e., If $\partial Ω$ is $C^{1, α}$ …

math.AP2018★ 10 cited

Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations

Yuanyuan Lian, Kai Zhang

In this paper, we study the boundary regularity for viscosity solutions of fully nonlinear elliptic equations. We use a unified, simple method to prove that if the domain $Ω$ satis…

math.AP2018

Boundary Hölder Regularity for Elliptic Equations on Reifenberg Flat Domains

Yuanyuan Lian, Kai Zhang

In this paper, we investigate the boundary Hölder regularity for elliptic equations (precisely, the Poisson equation, linear equations in divergence form and non-divergence form, t…

Asymptotic behavior at infinity of Weingarten surfaces

Interior BMO regularity for elliptic equations in divergence form

Boundary Hölder gradient estimates for parabolic p-Laplace type equations

Time derivative estimates for parabolic p-Laplace equations and applications to optimal regularity

Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets

Pointwise regularity for locally uniformly elliptic equations and applications

Interior pointwise Cα regularity for elliptic and parabolic equations with divergence-free drifts

Asymptotic behavior for fully nonlinear elliptic equations in exterior domains

Boundary pointwise regularity for fully nonlinear parabolic equations and an application to regularity of free boundaries

Boundary pointwise regularity and Liouville theorems for fully nonlinear equations on cones

A note on the BMO and Calderón-Zygmund estimate

Boundary pointwise regularity and applications to the regularity of free boundaries

Pointwise Boundary Differentiability for Fully Nonlinear Elliptic Equations

Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms

Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations

A simple proof of the transcendence of the trigonometric functions

On the boundary Hölder regularity for the infinity Laplace equation

Boundary Pointwise C1,α and C2,α Regularity for Fully Nonlinear Elliptic Equations

Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations

Boundary Hölder Regularity for Elliptic Equations on Reifenberg Flat Domains

Interior $B M O$ regularity for elliptic equations in divergence form

Boundary Hölder gradient estimates for parabolic $p$ -Laplace type equations

Time derivative estimates for parabolic $p$ -Laplace equations and applications to optimal regularity

Interior pointwise $C^{α}$ regularity for elliptic and parabolic equations with divergence-free drifts

Boundary Pointwise $C^{1, α}$ and $C^{2, α}$ Regularity for Fully Nonlinear Elliptic Equations