Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains
type: Item
instance of: scholarly article
title: Subelliptic estimates for the \(\overline\partial\)-Neumann operator on piecewise smooth strictly pseudoconvex domains
zbMATH Open document ID: 0953.32027
DOI: 10.1215/S0012-7094-98-09304-8
author: Joachim Michel
author: Mei-Chi Shaw
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: It is shown that the \(\overline \partial \)-Neumann operator \(N\) satisfies subelliptic estimates on a domain with piecewise smooth strictly pseudoconvex boundary, more precisely, it is shown that \(N\) maps \(L^2_{(p,q)}(\Omega)\) into \(H^{1/2}_{(p,q)}(\Omega)\) when \(1\leq q \leq n-1.\) Moreover the authors prove that \(\overline \partial N\) and \(\overline \partial * N\) have the same properties. It is also indicated that subellipticity does not imply regularity in other Sobolev spaces in this case, in contrast to smooth domains [\textit{J. J. Kohn} and \textit{L. Nirenberg}, Commun. Pure Appl. Math. 18, 443-492 (1965; Zbl 0125.33302)].
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 1425116
zbMATH Keywords: \(\overline \partial \)-Neumann operator
zbMATH Keywords: piecewise smooth strictly pseudoconvex domains
zbMATH Keywords: subelliptic estimates
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
cites work: Behavior of the Bergman projection on the Diederich-Fornæss worm
cites work: Sobolev estimates for the \({\bar \partial}\)-Neumann operator on domains in \({\mathbb{C}}^ n\) admitting a defining function that is plurisubharmonic on the boundary
cites work: Subelliptic estimates for the \({\bar \partial}\)-Neumann problem on pseudoconvex domains
cites work: Q4215046
cites work: Global 𝐶^{∞} irregularity of the ∂̄-Neumann problem for worm domains
cites work: Q3470840
cites work: Compactness of the Neumann operator for hyperconvex domains with non-smooth \(B\)-regular boundary
cites work: Q4891297
cites work: \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
cites work: Q3995750
cites work: The inhomogeneous Dirichlet problem in Lipschitz domains
cites work: Harmonic integrals on strongly pseudo-convex manifolds. I
cites work: Subellipticity of the \(\overline\partial\)-Neumann problem on pseudo- convex domains: sufficient conditions
cites work: Non‐coercive boundary value problems
cites work: Q5549989
cites work: Uniform estimates for the \(\bar\partial\)-equation on domains with piecewise smooth strictly pseudoconvex boundaries
cites work: Local existence theorems with estimates for \(\bar \partial_ b\) on weakly pseudo-convex CR manifolds
cites work: Q5607484
description: scientific article; zbMATH DE number 1425116