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Energy decreasing rearrangements of level sets preserving the domain and volume constrains

GFM seminar
CIUL, B1-01
2007-04-19 14:30 .. 15:30
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by José Maria Gomes (Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, IST)

Let $\Omega\subset R^"$ be a regular domain. We consider $C^"$ minimizers of the energy $\int_\Omega |\nabla u|^"$ under the constrain $\int_\Omega f(u)=C$ when $f$ is a $C^'$ non-negative function and $u=0$ in $\partial \Omega$. We provide a local correction of $u$ near a particular null-curvature point and conclude geometrical aspects of solutions to some variational elliptic BVP.