Boundary value problems for the Poisson equation and bi-analytic functions. (English) Zbl 1188.30058

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.


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
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