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

      Jun Zheng Zhihua Zhang Peihao Zhao

      Volume 123 Issue 3 August 2013 pp 373-382

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/123/03/0373-0382

    • Keywords

       

      Obstacle problem; free boundary; porosity; quasilinear elliptic equations.

    • Abstract

       

      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.

    • Author Affiliations

       

      Jun Zheng1 Zhihua Zhang2 Peihao Zhao3

      1. Basic Course Department, Emei Campus, Southwest Jiaotong University, Leshan, Sichuan 614202, China
      2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
      3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

    • Dates

       
      Published
      August 2013
      Manuscript received
      21 February 2012
      Manuscript revised
      13 April 2013

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