Spectral partition problems with volume and inclusion constraints

Autor:	Andrade, Pêdra D. S., Santos, Ederson Moreira dos, Santos, Makson S., Tavares, Hugo
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs 35B65 49J30 49J35
Druh dokumentu:	Working Paper
Popis:	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. Comment: From v1 to v2 we have clarified, corrected and simplified some arguments in Section 3 (Continuity of Minimizers). We also added more references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.02870 Zobrazit plný text záznamu View this record from Arxiv