Electron. J. Differential Equations, Vol. 2019 (2019), No. 97, pp. 1-22.

Entropy solutions to noncoercive nonlinear elliptic equations with measure data

Shuibo Huang, Tong Su, Xinsheng Du, Xinqiu Zhang

Abstract:
Let $\Omega\subseteq \mathbb{R}^N$ be a bounded domain. In this article, we investigate the existence of entropy solutions to the nonlinear elliptic problem

where $\mu$ is a diffuse measure with bounded variation on $\Omega$, $0\leq\theta<1$ is a positive constants, 1, $0<\lambda\leq p-1$, c(x) and b(x) belong to appropriate Lorentz spaces.

Submitted August 4, 2017. Published August 5, 2019.
Math Subject Classifications: 35R06, 35J70.
Key Words: Entropy solution; noncoercive; nonlinear elliptic equations; measure data.

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Shuibo Huang
School of Mathematics and Computer
Northwest Minzu University
Lanzhou, Gansu 730000, China
email: huangshuibo2008@163.com
Tong Su
School of Mathematics and Computer
Northwest Minzu University
Lanzhou, Gansu 730000, China
email: 309372469@qq.com
Xinsheng Du
School of Mathematical Sciences
Qufu Normal University
Qufu, Shandong 273165, China
email: duxinsheng1977@163.com
Xinqiu Zhang
School of Mathematics and Statistics
Qingdao University
Qingdao 266071, China
email: xinqiuzhang0220@163.com

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