紧致闭Riemann 流形上带梯度项的完全非线性椭圆方程的二阶导数估计

Bo Guan; Shujun Shi; Zhenan Sui

doi:10.1360/SSM-2020-0213

紧致闭Riemann 流形上带梯度项的完全非线性椭圆方程的二阶导数估计

Translated title of the contribution: Second order estimates for fully nonlinear elliptic equations with gradient terms on closed Riemannian manifolds

Bo Guan
, Shujun Shi^*
, Zhenan Sui

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations, which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.

Translated title of the contribution	Second order estimates for fully nonlinear elliptic equations with gradient terms on closed Riemannian manifolds
Original language	Chinese (Traditional)
Pages (from-to)	1721-1732
Number of pages	12
Journal	Scientia Sinica Mathematica
Volume	50
Issue number	12
DOIs	https://doi.org/10.1360/SSM-2020-0213
State	Published - Dec 2020

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abstract = "Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations, which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.",

keywords = "A priori estimate, Closed Riemannian manifold, Fully nonlinear elliptic equation",

author = "Bo Guan and Shujun Shi and Zhenan Sui",

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AU - Guan, Bo

AU - Shi, Shujun

AU - Sui, Zhenan

PY - 2020/12

Y1 - 2020/12

N2 - Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations, which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.

AB - Establishing a priori estimates for second derivatives is a key ingredient in the study of fully nonlinear elliptic equations, which is the focus of this paper. We consider a class of second order fully nonlinear equations on closed Riemannian manifolds. In terms of the tangent cone at infinity to the level sets of an associated function which may depend on the solution and its gradient, we introduce a condition to derive second order estimates for solutions of the equation.

KW - A priori estimate

KW - Closed Riemannian manifold

KW - Fully nonlinear elliptic equation

UR - https://www.scopus.com/pages/publications/85099050037

U2 - 10.1360/SSM-2020-0213

DO - 10.1360/SSM-2020-0213

M3 - 文章

AN - SCOPUS:85099050037

SN - 1674-7216

VL - 50

SP - 1721

EP - 1732

JO - Scientia Sinica Mathematica

JF - Scientia Sinica Mathematica

IS - 12

ER -

紧致闭Riemann 流形上带梯度项的完全非线性椭圆方程的二阶导数估计

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