Carleman condition for a degenerate second-order differential operator
type: Item
instance of: scholarly article
title: Carleman condition for a degenerate second-order differential operator
zbMATH Open document ID: 0667.35027
DOI: 10.1007/BF01066477
author: N. V. Belichkova
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: In \(R^ N\), \(N\geq 2\) a degenerate elliptic operator \[ Lu(x)=- \sum^{N}_{i=1}(\partial /\partial x_ i)(\alpha^ 2(x)\partial u(x)/\partial x_ i)+\beta (x)u(x) \] is investigated where \(\alpha (x)\in C^{\infty}(R^ N),\quad \beta (x)=\alpha^ 2(x)-\alpha (x)\Delta \alpha (x)+q(x),\) \(| \alpha (x)| \geq 0\), \(q(x)\in L_ 2(R^ N).\) It is proved that if degeneration is not very strong, namely, \(\alpha^{-1}(x)\in L_ 2(R^ N)\), then the minimal operator generated by the given elliptic expression is of Carleman type. The estimates are obtained for the kernel of the inverse which is an integral of the minimal operator.
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 4091987
zbMATH Keywords: minimal operator
zbMATH Keywords: Carleman type
zbMATH Keywords: estimates
zbMATH Keywords: kernel of the inverse
reviewed by: Bronius Kvedaras
MaRDI profile type: Publication
cites work: Distribution of eigenvalues and the Green functions of degenerated elliptic differential operators
cites work: Boundary value problems for some degenerate-elliptic operators
cites work: Q3265952
full work available at URL: https://doi.org/10.1007/bf01066477
OpenAlex ID: W2323565087
Recommended article: Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition
Recommended article: Carleman Estimates for a Class of Degenerate Parabolic Operators
Recommended article: Second-order operators with degenerate coefficients
Recommended article: Carleman Estimate for a General Second-Order Hyperbolic Equation
Recommended article: Carleman Estimates with Second Large Parameter for Second Order Operators
Recommended article: The Dirichlet boundary problem for second order parabolic operators satisfying a Carleson condition
Recommended article: Carleman Estimates for Second Order Partial Differential Operators and Applications
Recommended article: Q5293723
Recommended article: Degenerate second-order differential equations in Hilbert spaces
Recommended article: Le théorème de Hörmander pour des opérateurs du second ordre infiniment dégénérés avec des coefficients dépendant du temps
description: scientific article; zbMATH DE number 4091987