Kumar, Ajay; Prakash, Ravi Boundary value problems for the Poisson equation and bi-analytic functions. (English) Zbl 1188.30058 Complex Variables, Theory Appl. 50, No. 7-11, 597-609 (2005). Summary: Explicit representations of the solution to higher-order Poisson equation with Dirichlet boundary conditions are obtained. Especially the equations \(\partial^ 2_ {z\overline{z}}w=f\) with the boundary data \(w=\gamma_ 0\) and \(\partial_ {z\overline{z}}w=\gamma_ 1\) are solved. Cited in 2 Documents MSC: 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.) 35J56 Boundary value problems for first-order elliptic systems 35J08 Green’s functions for elliptic equations Keywords:Poisson equation; Dirichlet boundary condition; polyanalytic equations; Green’s functions PDFBibTeX XMLCite \textit{A. Kumar} and \textit{R. Prakash}, Complex Variables, Theory Appl. 50, No. 7--11, 597--609 (2005; Zbl 1188.30058) Full Text: DOI