# Optimal partitions for Robin Laplacian eigenvalues

created by bucur on 13 Mar 2018

[BibTeX]

preprint

Inserted: 13 mar 2018

Year: 2018

ArXiv: 1803.03813 PDF

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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