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
Kalmenov T. Suragan D. Kadirbek A.
2026Institute of Applied Mathematics of Baku State University
Applied and Computational Mathematics
2026#25Issue 1170 - 179 pp.
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.
Double Layer Potential , Green’s Function , Integral Representation of Solutions , Laplace Equation , Theory of Restrictions and Extensions
Text of the article Перейти на текст статьи
Institute of Mathematics and Mathematical Modeling, Shevchenko 28, Almaty, Kazakhstan
Department of Mathematics, Nazarbayev University, 53, Kabanbay batyr Ave., Astana, 010000, Kazakhstan
Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
Faculty of Mechanics and Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026