On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set

2021/08/09 by Ferraresso, Francesco, Provenzano, Luigi
#35J35 #35J40 #35P20 #5B25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2108.03969

Abstract

Let Ω be a bounded domain in \mathbb R² with smooth boundary ∂Ω, and let ω_h be the set of points in Ω whose distance from the boundary is smaller than h. We prove that the eigenvalues of the biharmonic operator on ω_h with Neumann boundary conditions converge to the eigenvalues of a limiting problem in the form of system of differential equations on ∂Ω.

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