Spectral Stability of the ∂-Neumann Laplacian: Domain Perturbations

2019/08/08 by Fu, Siqi, Zhu, Weixia
#32G05 #32W05 #35J25 #35P15 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.03256

Abstract

We study spectral stability of the ∂-Neumann Laplacian on a bounded domain in ℂⁿ when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the ∂-Neumann Laplacian on bounded pseudoconvex domains in ℂⁿ, lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D'Angelo type in ℂⁿ.

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