Remarks on Hausdorff measure and stability for the p-obstacle problem (1 < p < 2)

被引：4
|
作者：
Zhao, Peihao [1 ]
Zheng, Jun [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
来源：
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2012年 / 122卷 / 01期
关键词：
Obstacle problem; Hausdorff measure; stability; ELLIPTIC-EQUATIONS; FREE-BOUNDARIES; LAPLACIAN TYPE; POROSITY;
D O I：
10.1007/s12044-012-0053-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the obstacle problem for the inhomogeneous p-Laplace equation div(vertical bar del(u)vertical bar(P-2)del u) = f.chi{u>0}, 1 < p < 2, where f is a positive, Lipschitz function. We prove that the free boundary has finite (N - 1)-Hausdorff measure and stability property, which completes previous works by Caffarelli (J. Fourier Anal. Appl. 4(4-5) (1998) 383-402) for p = 2, and Lee and Shahgholian (J. Differ Equ. 195 (2003) 14-24) for 2 < p < infinity.
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页码：129 / 137
页数：9
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