Journal article
A free boundary problem for p-Laplacian in the plane
Journal of mathematical analysis and applications, Vol.380(1), pp.10-16
2011
DOI: 10.1016/j.jmaa.2011.03.027
Abstract
We consider the following free boundary problem in an unbounded domain
Ω in two dimensions:
Δ
p
u
=
0
in
Ω,
u
=
0
,
∂
u
∂
n
=
g
0
on
J
0
,
u
=
1
,
∂
u
∂
n
=
g
1
on
J
1
, where
∂
Ω
=
J
0
∪
J
1
. We prove that if
0
<
u
<
1
in
Ω,
J
i
is the graph of a function in
C
loc
1
,
α
(
R
)
and
g
i
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.
Details
- Title: Subtitle
- A free boundary problem for p-Laplacian in the plane
- Creators
- Lihe Wang - Department of Mathematics, University of Iowa, Iowa City, IA 52242, USALihzhou Wang - Department of Mathematics, School of Science, Xiʼan Jiaotong University, Xiʼan, Shaanxi Province 710049, Peopleʼs Republic of China
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.380(1), pp.10-16
- DOI
- 10.1016/j.jmaa.2011.03.027
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Grant note
- 10771166 / National Natural Science Foundation of China
- Language
- English
- Date published
- 2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984083897802771
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