Date:

2025-04-30

Title of Paper:

A free boundary problem for p-Laplacian in the plane

Journal:

J. Math. Anal. Appl., 380（2011）, 10-16.

Summary:

Abstract:
We  consider  the following free boundary problem in an unbounded
domain $Omega$ in two dimensions: $Delta_p u=0$ in  $Omega$,
$u=0, frac{partial{u}}{partial n}=g_0$ on $J_0$, $u=1,
frac{partial{u}}{partial n}=g_1$ on $J_1$, where
$partialOmega=J_0cup J_1$. We prove that if $0<u<1$ in $Omega$,
$J_i$ is the  graph of a function in $C^{1,alpha}_{loc}({
l})$ and
$g_i$ is a  constant for each $i=0,1$, then the free boundary
$partialOmega$ must be two parallel straight lines and the
solution $u$ must be a linear function. The proof is based on
  maximum principle.

Co-author:

Wang Lihe, Wang Lizhou

Translation or Not:

No

Date of Publication:

2011-11-11