Fundamental solutions for the Tricomi operator. II
type: Item
instance of: scholarly article
title: Fundamental solutions for the Tricomi operator. II
zbMATH Open document ID: 1017.35081
DOI: 10.1215/S0012-7094-02-11137-5
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
review text: The explicit calculation of the fundamental solutions for the Tricomi operator \({\mathfrak I}u=yu_{xx}+u_{yy}\) -- one of the simplest examples of a partial differential operator of mixed type -- is under consideration. It is shown that all such fundamental solutions originate from the hypergeometric function \(F(1/6,1/6; 1;\xi)\) that is obtained in the process of looking for homogeneous solutions to reduced hyperbolic Tricomi equation. For Part I, see ibid. 98, No. 3, 465-4-83 (1999; Zbl 0945.35063), and Correction to: ''Fundamental solutions for the Tricomi operator, II'', Duke Math. J. 117, No. 2, 385--387 (2002).
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 1820883
zbMATH Keywords: reduced hyperbolic Tricomi equation
author: J. Barros-Neto
author: I. M. Gel'fand
reviewed by: Elena Gavrilova
MaRDI profile type: Publication
cites work: Q3229615
cites work: Fundamental solutions for the Tricomi operator
cites work: Q5823354
cites work: Q5824493
cites work: Symmetric positive linear differential equations
cites work: Q5724171
cites work: Solutions élémentaires de certaines équations aux dérivées partielles du type mixte
cites work: La solution unitaire d'un opérateur différentiel linéaire. (Problème de Cauchy. II.)
cites work: Un prolongement de la transformation de Laplace qui transforme la solution unitaire d'un opérateur hyperbolique en sa solution élémentaire. (Problème de Cauchy. IV.)
cites work: A weak solution for a system of equations of elliptic-hyperbolic type
cites work: Q5795279
full work available at URL: s0012-7094-02-11137-5
OpenAlex ID: W4302889976
description: scientific article; zbMATH DE number 1820883