In thie paper we consider the following multiphase shape optimization problem min {∑i=1h λ1 (Ωi) + α|Ωi| : Ωi open, Ωi ⊂ D, Ωi ∩ Ωj = φ}, where α > 0 is a given constant and D ⊂ ℝ2 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.
A multiphase shape optimization problem for eigenvalues: Qualitative study and numerical results
Velichkov B.
2016-01-01
Abstract
In thie paper we consider the following multiphase shape optimization problem min {∑i=1h λ1 (Ωi) + α|Ωi| : Ωi open, Ωi ⊂ D, Ωi ∩ Ωj = φ}, where α > 0 is a given constant and D ⊂ ℝ2 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.File in questo prodotto:
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