Jonathan Rohleder Stockholms Universitet

From the hot spots conjecture to Neumann–Dirichlet eigenvalue comparison

Abstract:

Motivated by the famous hot spots conjecture, in this talk we discover a non-standard variational approach to the eigenvalues (and eigenfunctions) of the Neumann and Dirichlet Laplacian operators on bounded planar domains. A variant of this variational principle turns out to yield an inequality between Neumann and Dirichlet Laplacian eigenvalues on simply connected planar domains which previously only had been known for convex domains.