On the honeycomb conjecture for Robin Laplacian eigenvalues

2017/06/30 by Bucur, Dorin, Fragala, Ilaria · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1706.10055

Abstract

We prove that the optimal cluster problem for the sum of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity.

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