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Abstract
We consider the problem of minimizing the energy functional ∫(|∇u|2 + χ{u>0}). We show that the singular axissymmetric 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.
Received: 2006-04-04
Published Online: 2009-07-30
Published in Print: 2009-October
© Walter de Gruyter Berlin · New York 2009
