Porosity of Free Boundaries in the Obstacle Problem for Quasilinear Elliptic Equations

Proceedings Mathematical Sciences

Zhihua Zhang¹  Peihao Zhao²  Jun Zheng³ 

[1] School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 00, China$$;School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 0000, China$$;Basic Course Department, Emei Campus, Southwest Jiaotong University, Leshan, Sichuan 0, China$$

关键词: Obstacle problem;    free boundary;    porosity;    quasilinear elliptic equations.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, we establish growth rate of solutions near free boundaries in the identical zero obstacle problem for quasilinear elliptic equations. As a result, we obtain porosity of free boundaries, which is naturally an extension of the previous works by Karp et al. (J. Diff. Equ. 164 (2000) 110–117) for 𝑝-Laplacian equations, and by Zheng and Zhang (J. Shaanxi Normal Univ. 40(2) (2012) 11–13, 18) for 𝑝-Laplacian type equations.

【 授权许可】

Unknown