A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter

2018/10/14 by Bucur, D., Ferone, V., Nitsch, C. +1 · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1810.06108

Abstract

In this paper we prove that the ball maximizes the first eigenvalue of the Robin Laplacian operator with negative boundary parameter, among all convex sets of ℝⁿ with prescribed perimeter. The key of the proof is a dearrangement procedure of the first eigenfunction of the ball on the level sets of the distance function to the boundary of the convex set, which controls the boundary and the volume energies of the Rayleigh quotient.

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• On the optimization of the Robin eigenvalues in some classes of polygons

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