Spectral Stability of the $\overline{\partial}$-Neumann Laplacian: Domain Perturbations

Siqi Fu; Weixia Zhu

doi:10.1007/s12220-021-00769-z

Spectral Stability of the $\overline{\partial}$-Neumann Laplacian: Domain Perturbations

Siqi Fu
, Weixia Zhu (Corresponding author)

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in C ⁿ 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 C ⁿ, 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 C ⁿ.

Original language	English
Article number	57
Number of pages	34
Journal	Journal of Geometric Analysis
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s12220-021-00769-z
Publication status	Published - Feb 2022

Austrian Fields of Science 2012

101008 Complex analysis

Keywords

COMPACTNESS
Finite type condition
OPERATORS
PSEUDOCONVEX DOMAINS
Property (P)
Pseudoconvex domain
SUBELLIPTICITY
Spectrum
Stability
The partial derivative-Neumann Laplacian
Property (P)
The ∂¯ -Neumann Laplacian

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10.1007/s12220-021-00769-zLicence: CC BY 4.0

https://phaidra.univie.ac.at/o:1589253Licence: CC BY 4.0

Cite this

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title = "Spectral Stability of the \$\textbackslash{}overline\{\textbackslash{}partial\}\$-Neumann Laplacian: Domain Perturbations",

abstract = "We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in C n 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 C n, lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D{\textquoteright}Angelo type in C n. ",

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author = "Siqi Fu and Weixia Zhu",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2022",

month = feb,

doi = "10.1007/s12220-021-00769-z",

language = "English",

volume = "32",

journal = "Journal of Geometric Analysis",

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T1 - Spectral Stability of the $\overline{\partial}$-Neumann Laplacian: Domain Perturbations

AU - Fu, Siqi

AU - Zhu, Weixia

PY - 2022/2

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N2 - We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in C n 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 C n, 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 C n.

AB - We study spectral stability of the ∂¯ -Neumann Laplacian on a bounded domain in C n 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 C n, 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 C n.

KW - COMPACTNESS

KW - Finite type condition

KW - OPERATORS

KW - PSEUDOCONVEX DOMAINS

KW - Property (P)

KW - Pseudoconvex domain

KW - SUBELLIPTICITY

KW - Spectrum

KW - Stability

KW - The partial derivative-Neumann Laplacian

KW - Property (P)

KW - The ∂¯ -Neumann Laplacian

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DO - 10.1007/s12220-021-00769-z

M3 - Article

SN - 1050-6926

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 2

M1 - 57

ER -

Spectral Stability of the $\overline{\partial}$-Neumann Laplacian: Domain Perturbations

Abstract

Austrian Fields of Science 2012

Keywords

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