A free boundary problem for p-Laplacian in the plane

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

Wang Lihe²  Wang Lihzhou¹ 

[1] Xi An Jiao Tong Univ, Sch Sci, Dept Math, Xian 710049, Shaanxi Prov, Peoples R China

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

关键词: p-Laplacian;    Free boundary;    Maximum principle;   

DOI  :  10.1016/j.jmaa.2011.03.027

来源: Elsevier

【 摘 要 】

We consider the following free boundary problem in an unbounded domain in two dimensions: Delta(p)u =0 in Omega, u =0, partial derivative u/partial derivative n =g(0) on J(0), u =1, partial derivative u/partial derivative n =g(1) on J(1), where partial derivative Omega = J(0) boolean OR J(1) We prove that if 0 < u < 1 in Omega , J(1) is the graph of a function in C-loc(1,alpha) and gi is a constant for each i = 0, 1, then the free boundary partial derivative Omega must be two parallel straight lines and the solution u must be a linear function. The proof is based on maximum principle. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free