科研论文 - 王 立周
论文标题 | A Liouville type theorem for a variational problem with free boundary in dimension three |
作者 | Wang Lizhou |
发表/完成日期 | 2012-04-01 |
期刊名称 | Nonlinear analysis, 75(2012), 4062-4067. |
期卷 | |
相关文章 | |
论文简介 | 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$. |