Approximation of solutions of linear PDE with analytic coefficients
type: Item
instance of: scholarly article
title: Approximation of solutions of linear PDE with analytic coefficients
zbMATH Open document ID: 0552.35009
DOI: 10.1215/S0012-7094-83-05013-5
published in: Duke Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The paper establishes an approximation formula for distribution solutions in open sets in \(R^{n+1}\) of a first-order system of homogeneous linear partial differential equations with analytic coefficients. Actually it is shown that any such solution is the limit, in the appropriate distribution sense, of a sequence of analytic solutions of the same equations, where the approximators are expressed in terms of the Cauchy data of the original solution. The proof relies on the techniques of analytic pseudodifferential and Fourier integral operators. Essential tools are the microlocalization and the assumption that all the complex characteristics of the differential operator are simple.
Mathematics Subject Classification ID: 35F10
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 47Gxx
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3879371
zbMATH Keywords: approximation formula
zbMATH Keywords: distribution solutions
zbMATH Keywords: analytic coefficients
zbMATH Keywords: Cauchy data
zbMATH Keywords: microlocalization
zbMATH Keywords: complex characteristics
author: Mohamed Salah Baouendi
author: François Treves
reviewed by: M. Kracht
MaRDI profile type: Publication
cites work: A property of the functions and distributions annihilated by a locally integrable system of complex vector fields
cites work: Q3900553
cites work: Q3662334
full work available at URL: s0012-7094-83-05013-5
OpenAlex ID: W1559840036
description: scientific article; zbMATH DE number 3879371