| Abstract: |
| In the calculus of variations symmetrization techniques are useful for estimating
the energy or the Rayleigh quotient provided the solutions of the underlying problems
satisfy a Dirichlet boundary condition. The ball is then the optimal domain.
In the case of Robin boundary conditions symmetrization is not applicable in general,
and the question whether or not the ball is optimal is not clear. We focus on
on nearly spherical domains and study how much their solutions differ from the ones in the ball.
This talk is based on a study in collaboration with Alfred Wagner. |
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