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论文期刊

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   
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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$.
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