Spectral partition problems with volume and inclusion constraints
Analysis of PDEs
2023-06-22 v2
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.
Cite
@article{arxiv.2305.02870,
title = {Spectral partition problems with volume and inclusion constraints},
author = {Pêdra D. S. Andrade and Ederson Moreira dos Santos and Makson S. Santos and Hugo Tavares},
journal= {arXiv preprint arXiv:2305.02870},
year = {2023}
}
Comments
From v1 to v2 we have clarified, corrected and simplified some arguments in Section 3 (Continuity of Minimizers). We also added more references