A free boundary problem for p-Laplacian in the plane

作者：Wang Lihe; Wang Lihzhou^*

来源：Journal of Mathematical Analysis and Applications, 2011, 380(1): 10-16.

DOI：10.1016/j.jmaa.2011.03.027

• p-Laplacian
• Free boundary
• Maximum principle

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.

• 出版日期2011-8-1
• 单位西安交通大学