A free boundary problem for p-Laplacian in the plane |
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| Authors: | Lihe Wang |
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| Affiliation: | a Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
b Department of Mathematics, School of Science, Xi?an Jiaotong University, Xi?an, Shaanxi Province 710049, People?s Republic of China |
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| Abstract: | We consider the following free boundary problem in an unbounded domain Ω in two dimensions: Δpu=0 in Ω,  on J0,  on J1, where ∂Ω=J0∪J1. We prove that if 0<u<1 in Ω, Ji is the graph of a function in  and gi is a constant for each i=0,1, then the free boundary ∂Ω must be two parallel straight lines and the solution u must be a linear function. The proof is based on maximum principle. |
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| Keywords: | p-Laplacian Free boundary Maximum principle |
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