Dirichlet and Neumann eigenvalue problems on CR manifolds
type: Item
instance of: scholarly article
title: Dirichlet and Neumann eigenvalue problems on CR manifolds
zbMATH Open document ID: 1405.32057
author: Amine Aribi
author: Sorin Dragomir
published in: Ricerche di Matematica
publication date: 2018-11-22T00:00:00Z
review text: The main results in this paper are solutions to the Dirichlet and Neumann problems for the sub-Laplacian on domains in CR manifolds. Let \(M\) be a strictly pseudoconvex CR manifold, \(\theta\) be a positively oriented contact form on \(M\) and \(d_{\theta}\) be a Carnot-Carathéodory metric on \((M,\theta)\). The authors prove that the weak Dirichlet problem for the sub-Laplacian can be solved on domains supporting the Poincaré inequality, and the weak Neumann problem can be solved on \(C^{1,1}\) connected \((\epsilon, \delta)\) domains in the Heisenberg group. As an application the authors show the discretness of the Dirichlet and Neumann spectra for the sub-Laplacian on bounded domains of Carnot-Carathéodory complete pseudohermitian manifolds.
reviewed by: Koichi Saka
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 35H20
zbMATH DE Number: 6983424
zbMATH Keywords: CR manifolds
zbMATH Keywords: Poincaré inequality
zbMATH Keywords: Carnot-Carathéodory metric
zbMATH Keywords: sub-Laplacian
zbMATH Keywords: Dirichlet and Neumann problems
MaRDI profile type: Publication
full work available at URL: s11587-018-0420-x
OpenAlex ID: W2885143092
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Wikidata QID: Q129422850
DOI: 10.1007/S11587-018-0420-X
description: scientific article; zbMATH DE number 6983424