An optimal partition problem for the localization of eigenfunctions
Guy David, Hassan Pourmohammad · Mathematika · 2022
We study the minimizers of a functional on the set of partitions of a domain into N subsets of locally finite perimeter in Ω, whose main term is . Here the positive bounded function a may, for instance, be related to the Landscape function of some Schrödinger operator. We prove the existence of minimizers through the equivalence with a weak formulation, and the local Ahlfors regularity and uniform rectifiability of the boundaries .