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.

引用

页码：129 / 137

页数：9

共 8 条

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

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