Date:

2025-04-30

Title of Paper:

A Liouville type theorem for a variational problem with free boundary in dimension three

Journal:

Nonlinear analysis, 75（2012）, 4062-4067.

Summary:

abstract
We consider the minimum problem for the functional
[E_Omega(u)=int_{Omega}(|Du|^2+lambda^2ind{{u>0}})]
in three dimensional space, where $lambda>0$ is a constant. We will establish  a Liouville type theorem for this variational problem: if $uin C(
l^3)$ is a nonnegative and nonzero global minimizer,
then $u(x)=lambda((x-x_0)cdot
u)^+$ for  some point $x_0$ and some unit vector $
u$.

Co-author:

Wang Lizhou

Translation or Not:

No

Date of Publication:

2012-04-01