On Necessary and Sufficient Conditions for the Existence of a Classical Solution of an Inhomogeneous Cauchy–Riemann System

Abstract

The question of necessary and sufficient conditions for the existence of a classical solution of inhomogeneous Cauchy–Riemann systems in a domain bounded by a piecewise smooth contour is studied. It is proved that the condition of the uniform stronger continuity of that inhomogeneity is a necessary condition, but it is also a sufficient condition if the inhomogeneity belongs to the L₁ space.