Spectral partition problems with volume and inclusion constraints

2023/05/04 by Andrade, Pêdra D. S., Santos, Ederson Moreira dos, Santos, Makson S. +1 · 2 citations
#35B65 #49J30 #49J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.02870

Abstract

In this paper, we discuss a class of spectral partition problems with a measure constraint, for partitions of a given bounded connected open set. We establish the existence of an optimal open partition, showing that the corresponding eigenfunctions are locally Lipschitz continuous, and obtain some qualitative properties for the partition. The proof uses an equivalent weak formulation that involves a minimization problem of a penalized functional where the variables are functions rather than domains, suitable deformations, blowup techniques, and a monotonicity formula.

Cited by

• A survey on the optimal partition problem
• Spectral minimal partitions of unbounded domains

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