On a Method for Transforming the Double Layer Potential to a Volume Potential and its Application to the Description of Coercive Problems for the Laplace Equation (pp.170-179)

In this work, a method for transforming the double layer potential into a volume potential is presented. This new approach is applied to the study of non-classical boundary value problems for the Laplace equation, particularly those of Bitsadze-Samarskii type, where boundary conditions involve values inside the domain. The method also addresses boundary value problems with non-local boundary conditions, where traditional techniques are less effective. The results contribute to the broader theory of correct boundary extensions and restrictions of differential operators and offer a new tool for analyzing various elliptic problems. © 2026, Institute of Applied Mathematics of Baku State University. All rights reserved.