A Boundary Value Problem for the Laplace Equation on a Plane with a Peculiarity in the Least Coefficient
DOI:
https://doi.org/10.52575/2687-0959-2026-58-2-168-175Keywords:
Laplace Equation, Polar Singularity, Dirichlet ProblemAbstract
In a bounded domain on a plane, a second-order elliptic equation with a polar singularity in the lower-order coefficient is considered, whose principal operator is the Laplace operator. The problem of constructing an explicit integral representation of the general solution is studied. The case with a first-order polar singularity is considered separately using a modified Pompeiu – Vekua integral. The obtained integral representation is applied to find the unique solution of the Dirichlet-type problem. The obtained explicit solution of the considered equation also allows for the direct formulation and investigation of linear conjugation and Riemann – Hilbert type problems.
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