Optimal partitions for Robin Laplacian eigenvalues

2018/03/10 by Bucur, Dorin, Fragalà, Ilaria, Giacomini, Alessandro
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.03813

Abstract

We prove the existence of an optimal partition for the multiphase shape optimization problem which consists in minimizing the sum of the first Robin Laplacian eigenvalue of k mutually disjoint \it open sets which have a \mathcal H ^ d-1-countably rectifiable boundary and are contained into a given box D in R^d

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