On the three-dimensional Riemann function
type: Item
instance of: scholarly article
title: On the three-dimensional Riemann function
zbMATH Open document ID: 0880.45001
DOI: 10.1007/BF02673035
author: V. I. Zhegalov
published in: Siberian Mathematical Journal
publication date: 1998-01-05T00:00:00Z
review text: A Riemann function of the equation \[ {\mathfrak L}u \equiv u_{xyz} + au_{xy} + bu_{yz} + cu_{xz} + du_x + eu_y + fu_z + gu = 0 \eqno{(1)} \] is defined to be a solution to the formally adjoint equation satisfying supplementary conditions related to the coefficients of (1). The coefficients depend on \(x\), \(y\), and \(z.\) In the article, some properties of the above Riemann function are indicated and, on this basis, suitable integral equations are obtained for its determination. In a number of cases, the author succeeds in constructing a Riemann function explicitly.
Mathematics Subject Classification ID: 45A05
zbMATH DE Number: 1099641
zbMATH Keywords: Riemann function
zbMATH Keywords: three-dimensional partial differential equation
zbMATH Keywords: integral equation
MaRDI profile type: Publication
cites work: Q4283897
cites work: Q3258018
description: scientific article; zbMATH DE number 1099641