Dirichlet Problem for a Generalized Cauchy–Riemann Equation with a Supersingular Point on a Half-Plane

Abstract

For equations with a Cauchy–Riemann operator involving a strong point singularity in the lower coefficient on a half-plane, an integral representation of the solution is obtained in the class of bounded functions and a Dirichlet-type problem is studied. The calculation of the Vekua–Pompeiu integral is examined in the case when the density of the integral has strong singularities in a set of points or lines.