Second order differential operators and Dirichlet integrals with singular coefficients. I: Functional calculus of one-dimensional operators
type: Item
instance of: scholarly article
title: Second order differential operators and Dirichlet integrals with singular coefficients. I: Functional calculus of one-dimensional operators
zbMATH Open document ID: 0653.35034
author: Bernard Gaveau
author: Masami Okada
author: Tatsuya Okada
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: Let a,c be piecewise \(C^ 1\), \(C^ 0\) functions on \({\mathbb{R}}\) respectively. The authors study the parabolic Cauchy problem \[ \partial u/\partial t=Lu\quad if\quad t>0,\quad u|_{t=0}=0, \] where \(Lu=(1/c^ 2)\partial_ x(1/a\) \(2)\partial_ xu)\) (and also Cauchy problems for wave or Schrödinger equations). Explicit formulas for the heat kernel are given. The case where L is a spherically symmetric elliptic operator in \({\mathbb{R}}^ 3\) is also treated.
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 4065512
zbMATH Keywords: singular coefficients
zbMATH Keywords: parabolic Cauchy problem
zbMATH Keywords: Schrödinger equations
zbMATH Keywords: Explicit formulas
zbMATH Keywords: heat kernel
zbMATH Keywords: spherically symmetric
reviewed by: Paul Godin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4065512