Electron. J. Differential Equations, Vol. 2017 (2017), No. 120, pp. 1-13.

Lorentz estimates for asymptotically regular fully nonlinear elliptic equations

Yongyong Wang, Junjie Zhang, Shenzhou Zheng

Abstract:
We prove a global Lorentz estimate of the Hessian of strong solutions to a class of asymptotically regular fully nonlinear elliptic equations over a $C^{1,1}$ smooth bounded domain. Here, the approach of the main proof is based on the Possion's transform from an asymptotically regular elliptic equation to the regular one.

Submitted October 25, 2016. Published May 4, 2017.
Math Subject Classifications: 35J60, 35B65, 35D30.
Key Words: Nonlinear elliptic equations; Lorentz estimate; asymptotically regular; small BMO coefficients.

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Yongyong Wang
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: yongyongwang@bjtu.edu.cn
Junjie Zhang
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: junjiezhang@bjtu.edu.cn
Shenzhou Zheng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044, China
email: shzhzheng@bjtu.edu.cn

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