A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
In thie paper we consider the following multiphase shape optimization problem $\min\big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ {open},\ \Omega_i\subset D, \Omega_i\cap\Omega_j=\emptyset\big\}$, where $\alpha>0$ is a given constant and $D\subset\mathbb{R}^2$ 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 …