# A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results

arXiv: https://arxiv.org/abs/1606.02513 · HTML: https://mlsanity.com/paper/1606.02513/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 1 of 1)

- [WANCO: Weak Adversarial Networks for Constrained Optimization problems](https://mlsanity.com/paper/2407.03647/) (2024)

## Abstract (arXiv)

We consider the multiphase shape optimization problem minBigsumi=1hλ1(Omegai)+α|Omegai|: Omegai hboxopen, Omegaisubset D, OmegaicapOmegaj=emptysetBig, where α>0 is a given constant and  DsubsetBbbR2 is a bounded open set with Lipschitz boundary. We give some new results concerning the qualitative properties of the optimal sets and the regularity of the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.