A minimum problem with free boundary for a degenerate quasilinear operator期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A minimum problem with free boundary for a degenerate quasilinear operator

Authors:	Donatella Danielli Arshak Petrosyan

Affiliation:	(1) Department of Mathematics, Purdue University, IN 47907 West Lafayette, USA;(2) Department of Mathematics, University of Texas at Austin, TX 78712 Austin, USA

Abstract:	In this paper we prove $C^{1,alpha}$ regularity (near flat points) of the free boundary in the Alt-Caffarelli type minimum problem for the p-Laplace operator: $J(u)=int_Omegaleft( \|nabla u\|^p + lambda^pchi_{{u>0}}right)dxrightarrow minqquad (1<p<infty).$ Received: 3 June 2003, Accepted: 9 June 2004, Published online: 8 February 2005Mathematics Subject Classification (2000): 35R35, 35J60The first author is partially supported by NSF Grant DMS-0202801 and NSF CAREER Grant DMS-0239771

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