Fundamental solutions for second order subelliptic operators
type: Item
instance of: scholarly article
title: Fundamental solutions for second order subelliptic operators
zbMATH Open document ID: 0613.35002
DOI: 10.2307/1971278
author: Antonio Sánchez-Calle
author: Charles Fefferman
published in: Annals of Mathematics. Second Series
publication date: 1986-01-01T00:00:00Z
review text: This paper deals with the fundamental solution of a second-order linear partial differential operator L on a compact manifold M with smooth measure \(\mu\). In local coordinates \[ L=- \sum^{n}_{i,j=1}a^{ij}(x)\partial x_ i\partial x_ j+\sum^{n}_{k=1}b^ k(x)\partial x_ k+c(x), \] where \((a^{ij})\), \((b^ k)\), c are real, \(n>2\), the matrix \((a^{ij}(x))\) is positive semidefinite, and L is subelliptic. The author investigates the behavior of the fundamental solution G(x,y) near \(x=y\) and finds out its estimates. Furthermore, the author gets some new estimates for solution of the equation \(Lu=f\).
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35G05
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 58J99
zbMATH DE Number: 3991986
zbMATH Keywords: fundamental solution
zbMATH Keywords: compact manifold
zbMATH Keywords: smooth measure
zbMATH Keywords: subelliptic
zbMATH Keywords: estimates
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/1971278
OpenAlex ID: W2313063242
description: scientific article; zbMATH DE number 3991986