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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