BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Minimal $k$-partition for the $p$-norm of the eigenvalues Bonnaillie-Noël, Virginie


In this talk,we analyze the connections between the nodal domains of the eigenfunctions of the Dirichlet-Laplacian and the partitions of the domain by $ k$ open sets $D_i$ which are minimal in the sense that the maximum over the $D_i$'s of the groundstate energy of the Dirichlet realization of the Laplacian is minimal. Instead of considering the maximum among the first eigenvalues, we can also consider the $p$-norm of the vector composed by the first eigenvalues of each subdomain.

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