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"A variational approach to isoperimetric inequalities" January 27, 2011 (10:00 AM PST - 10:45 AM PST)
Parent Program: --
Location: MSRI: Baker Board Room
Speaker(s) Dorin Bucur
Description Abstract: A variational approach to solve an isoperimetric inequality may read:
  - prove the existence of an optimal shape without imposing any a priori smoothness  constraint. A relaxation phenomenon may be observed, the solution being a measure or a quasi-open set.
  - study the regularity of the optimal shape. This is a difficult problem,  but sometimes mild regularity may be enough to extract optimality conditions.
  - write optimality conditions and get qualitative information on the optimal shape.
  I will give some recent results involving the eigenvalues of the Laplace operator with Robin boundary conditions and I will discuss both the optimal design and the free boundary points of view.
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