On normality of some elliptic functional differential operators
type: Item
instance of: scholarly article
title: On normality of some elliptic functional differential operators
zbMATH Open document ID: 0924.35188
DOI: 10.1007/BF02466060
author: A. L. Skubachevskii
publication date: 1999-11-11T00:00:00Z
review text: The author obtains necessary and sufficient conditions for normality of the elliptic functional differential operators defined by \(A=A_0+A_1\), where \(A_0v= \Delta v\), \(v\in D(A_0)\) \[ D(A_0)= \bigl\{v\in W^2_2 (Q):Bv= 0\bigr\}, \] \(Bv=v |_{\partial \Omega}\) or \(Bv= {\partial v\over \partial\nu} |_{\partial Q}\); \(A_1v(x)= av(g(x)), a\neq 0\), \(a\in\mathbb R\) and \(g\) is a transformation of class \(C^3\) mapping a bounded domain \(V\subset \mathbb R^n\) onto \(g(V)\) such that \(| J_g(x) |\neq 0\) and \(g(Q)\subset Q\), \(Q\) being a bounded domain in \(\mathbb R^n\).
reviewed by: Drumi Bainov
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 35J99
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 1226008
zbMATH Keywords: necessary and sufficient conditions for normality
zbMATH Keywords: elliptic functional differential operators
MaRDI profile type: Publication
cites work: Elliptic functional differential equations and applications
cites work: Diffractive patterns in a nonlinear optical two-dimensional feedback system with field rotation
cites work: Q5549989
cites work: Q5526485
cites work: Q5667036
full work available at URL: https://doi.org/10.1007/bf02466060
OpenAlex ID: W2063179590
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1226008