On the three-dimensional Riemann function
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.
three-dimensional partial differential equation
scientific article; zbMATH DE number 1099641