Electron. J. Diff. Equ., Vol. 2016 (2016), No. 142, pp. 1-13.

Lorentz estimates for asymptotically regular elliptic equations in quasiconvex domains

Junjie Zhang, Shenzhou Zheng

Abstract:
We derive a global Lorentz estimate of the gradient of weak solutions to nonlinear elliptic problems with asymptotically regular nonlinearity in quasiconvex domains. Here, we prove its Lorentz estimate for such an asymptotically regular elliptic problem by constructing a regular problem via Poisson's formula, and quasiconvex domain locally approximated by convex domain.

Submitted October 2, 2015. Published June 14, 2016.
Math Subject Classifications: 35J60, 35B65, 35D30.
Key Words: Lorentz estimate; Poisson kernel; Lorentz space; regularity.

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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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