Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
type: Item
instance of: scholarly article
title: Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
zbMATH Open document ID: 0892.35031
author: Hans-Christoph Grunau
author: Guido Sweers
published in: Mathematische Annalen
publication date: 1998-05-26T00:00:00Z
review text: Based on Boggio's formula the authors derive estimates for Green's functions of polyharmonic operators in balls \(B\). These estimates are delicate and require a subtle analysis. Different types of maximum principles are then derived. At first, boundary value problems of the type \[ ((-\triangle)^m+A)u=f \text{ in }B, \;D_mu=0 \text{ on } \partial B, \] where \(A\) is a perturbation of the polyharmonic operator, are considered. Conditions are given which insure that a positive \(f\) implies that the solution is also positive. The same question is discussed for systems of equations. The use of the Neumann series plays a crucial role.
reviewed by: Catherine Bandle
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 1031509
zbMATH Keywords: Green's function of polyharmonic operators
zbMATH Keywords: Boggio's formula
zbMATH Keywords: Neumann series
MaRDI profile type: Publication
full work available at URL: s002080050052
OpenAlex ID: W2140831171
DOI: 10.1007/S002080050052
description: scientific article; zbMATH DE number 1031509