Glasnik Matematicki, Vol. 60, No. 1 (2025), 89-106. \( \)

SUMMABILITY OF SOLUTIONS TO SOME DEGENERATE ELLIPTIC EQUATIONS

Aiping Zhang, Pengzhen Tian and Hongya Gao

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
e-mail:zhangaiping015@163.com

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
e-mail:pengzhentian0415@163.com

College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
e-mail:ghy@hbu.cn

Abstract.   This paper deals with boundary value problems for elliptic equations with degenerate coercivity whose prototype is \[ \left\{\begin{array}{ll} -\mbox {div} \left( a(x)|\nabla u (x)|^{p-2} \nabla u(x)\right) = f(x), & x \in \Omega, \\ u(x) = 0, & x \in {\partial \Omega}, \end{array}\right. \] with \(0\lt a(x) \le \beta\). Some summability properties of solutions are given.

2020 Mathematics Subject Classification.   35J70

Key words and phrases.   Elliptic equation, degenerate coercivity, weak solution, entropy solution.

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https://doi.org/10.3336/gm.60.1.06

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