The mixed Cauchy problem for holomorphic partial differential operators
type: Item
instance of: scholarly article
title: The mixed Cauchy problem for holomorphic partial differential operators
zbMATH Open document ID: 0836.35034
DOI: 10.1007/BF02788774
author: Peter Ebenfelt
author: H. S. Shapiro
published in: Journal d'Analyse Mathématique
publication date: 1996-04-29T00:00:00Z
review text: This paper deals with linear partial differential equations with analytic coefficients and the problem of finding holomorphic solutions which take prescribed values on each of an appropriate number of irreducible analytic hypersurfaces. The analysis proposed in the paper is local. It is interesting to note that even local existence for the mixed Cauchy problem is not valid in general although existence results are proved in some particular situations. As it concerns uniqueness of solutions it depends only on the principal part of the operator and the tangent hyperplanes of the initial manifolds. The authors illustrate their assertions with new results for the Laplace operator.
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35G15
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 807409
zbMATH Keywords: mixed Cauchy problem
Wikidata QID: Q105975031
reviewed by: Peter R. Popivanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02788774
OpenAlex ID: W2035451069
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description: scientific article; zbMATH DE number 807409