Calculus of Variations and Geometric Measure Theory

D. Bucur - I. FragalĂ  - A. Giacomini

Optimal partitions for Robin Laplacian eigenvalues

created by bucur on 13 Mar 2018



Inserted: 13 mar 2018

Year: 2018

ArXiv: 1803.03813 PDF


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 $R^d$