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

作者：Wang Lizhou^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2012, 75(10): 4062-4067.

DOI：10.1016/j.na.2012.02.022

• Liouville type theorem
• Variational problem
• Free boundary

We consider the minimum problem for the functional
E-Omega(u) = integral(Omega)(vertical bar Du vertical bar(2) + lambda(2) chi({u>0}))
in three dimensional space, where lambda > 0 is a constant. We will establish a Liouville type theorem for this variational problem: if u is an element of C(R-3) is a nonnegative and nonzero global minimizer, then u(x) = lambda((x - x(0)) . nu)(+) for some point x(0) and some unit vector nu.

• 出版日期2012-6
• 单位西安交通大学