A MULTIPHASE SHAPE OPTIMIZATION PROBLEM FOR EIGENVALUES: QUALITATIVE STUDY AND NUMERICAL RESULTS

作者：Bogosel Beniamin^*; Velichkov Bozhidar^*

来源：SIAM Journal on Numerical Analysis, 2016, 54(1): 210-241.

DOI：10.1137/140976406

• shape optimization
• multiphase
• eigenvalues
• optimal partition

In thie paper we consider the following multiphase shape optimization problem min {Sigma(h)(i-1) lambda(1)(Omega(i)) + alpha vertical bar Omega(i)vertical bar : Omega(i) open, Omega(i) subset of D, Omega(i) boolean AND Omega(j) = (sic) where alpha > 0 is a given constant and D subset of 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 the corresponding eigenfunctions. We also provide numerical results for the optimal partitions.

• 出版日期2016