A note on domain monotonicity for the Neumann eigenvalues of the Laplacian

2022/02/08 by Funano, Kei · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2202.03598

Abstract

Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian of a convex domain.

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