Compactness of the ∂-Neumann operator on the intersection of two domains

2014/08/26 by Mustafa Ayyürü, Ayyürü, Mustafa, Emil J. Sträube +2
Mathematics · #32W05 #35N15 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32W05 #msc:35N15

paper · pdf · doi:10.48550/arxiv.1408.6134

arxiv created 2014/08/26 · openalex publication_date 2014/08/26 · arxiv updated 2014/08/27 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

Abstract

Assume that Ω₁ and Ω₂ are two smooth bounded pseudoconvex domains in ℂ² that intersect (real) transversely, and that Ω₁ ∩ Ω₂ is a domain (i.e. is connected). If the ∂-Neumann operators on Ω₁ and on Ω₂ are compact, then so is the ∂-Neumann operator on Ω₁ ∩ Ω₂. The corresponding result holds for the ∂-Neumann operators on (0,n-1)-forms on domains in ℂⁿ.

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