Yuxia Tong, Shuang Liang, Shenzhou Zheng
Abstract:
This article concerns the higher integrability of a very weak solution
for
to the
Dirichlet problem of the nonlinear elliptic system
where
for
and
,
and each entry of
for
satisfies the monotonicity and controllable growth. If
for q>r, then we derive that the very weak solution u of above-mentioned
problem is integrable with
provided that r is sufficiently close to p, where
.
Submitted December 16, 2017. Published January 2, 2019.
Math Subject Classifications: 35D30, 35K10.
Key Words: Integrability; very weak solution; nonlinear elliptic system;
controllable growth.
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Yuxia Tong Department of Mathematics Beijing Jiaotong University Beijing 100044, China email: tongyuxia@bjtu.edu.cn | |
Shuang Liang Department of Mathematics Beijing Jiaotong University Beijing 100044, China email: shuangliang@bjtu.edu.cn | |
Shenzhou Zheng Department of Mathematics Beijing Jiaotong University Beijing 100044, China email: shzhzheng@bjtu.edu.cn |
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