A Singular Energy Minimizing Free Boundary
نویسندگان
چکیده
We consider the problem of minimizing the energy functional R (|∇u|2 + χ{u>0}). We show that the singular axisymmetric critical point of the functional is an energy minimizer in dimension 7. This is the first example of a non-smooth energy minimizer. It is analogous to the Simons cone, a least area hypersurface in dimension 8.
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تاریخ انتشار 2005