Green's functions for some highly degenerate elliptic operators
type: Item
instance of: scholarly article
title: Green's functions for some highly degenerate elliptic operators
zbMATH Open document ID: 0947.35078
author: Bernard Gaveau
author: Richard Beals
author: Peter C. Greiner
published in: Journal of Functional Analysis
publication date: 2000-11-06T00:00:00Z
review text: Let \(x\in\mathbb{R}^n\), \(t\in \mathbb{R}^m\), \(n,m,k\in \mathbb{N}\) and consider \(L:= \Delta_x+ b^{2k-2}\Delta_t\), \(b(x,t):= |x|\). Looking for an explicit Green's function \(K\) for \(L\), the authors obtain \(K(x,t; y,s)= R^{-(n+ mk-2)/2k} F(p,\rho)\) where \(R:= |x|^{2k}+|y|^{2k}+ k^2|t-s|^2\), \(\rho:= |x|^k|y|^k R^{-1}\), \(p:= \langle x,y\rangle R^{-1/k}\) and \(F:= F_{nmk}\) is a function given explicitly in the form of an algebraic expression for \(m\) even resp. of an definite integral for \(m\) odd.
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35J50
zbMATH DE Number: 1319967
zbMATH Keywords: Green's function
zbMATH Keywords: fundamental solution
zbMATH Keywords: degenerate elliptic operators
reviewed by: Norbert Weck
MaRDI profile type: Publication
OpenAlex ID: W2029945423
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DOI: 10.1006/JFAN.1999.3421
description: scientific article; zbMATH DE number 1319967