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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Spectral shape optimization problems with Neumann conditions on the free boundary
Spectral shape optimization problems with Neumann conditions on the free boundaryAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact INI IT. This talk has been canceled/deleted In this talk I will discuss the question of the maximization of the $k$-th eigenvalue of the Neumann-Laplacian under a volume constraint. After an introduction to the topic I will discuss the existence of optimal geometries. For now, there is no a general existence result, but one can prove existence of an optimal {\it (over) relaxed domain}, view as a density function. In the second part of the talk, I will focus on the low eigenvalues. The first non-trivial one is maximized by the ball, the result being due to Szego and Weinberger in the fifties. Concerning the second non-trivial eigenvalue, Girouard, Nadirashvili and Polterovich proved that the supremum in the family of planar simply connected domains of $R^2$ is attained by the union of two disjoint, equal discs. I will show that a similar statement holds in any dimension and without topological restrictions. This talk is part of the Isaac Newton Institute Seminar Series series. This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
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