@article{Sybil_2024, title={On the boundary integral equation method of solving boundary value problems for the two dimensional Laplace equation}, volume={62}, url={http://matstud.org.ua/ojs/index.php/matstud/article/view/330}, DOI={10.30970/ms.62.1.60-76}, abstractNote={<p>We consider approach based on the integral representation of solutions<br>in domain which consists of bounded and unbounded parts that<br>gives us opportunity to reduce different transmission type problems to<br>connected with them equivalent boundary equations of the first and the second kind.<br>We suppose also that solutions of some of these boundary problems are unbounded at infinity.<br>Interior and exterior Dirichlet and Neumann boundary value<br>problems for Laplace equation are restrictions of the solutions<br>os more general this transmission problems.<br>Interior Neumann and exterior Dirichlet boundary value problems we also can solve using<br>integral equation of the second kind that have not unique solution.<br>Corresponding modified equations are constructed in this case and solutions of obtained equations are unique.<br>We also show correctness of all obtained boundary equations of the second type<br>given on closed Lipschitz curve in some Hilbert spaces<br>without compactness of corresponding integral operators.</p>}, number={1}, journal={Matematychni Studii}, author={Sybil, Yu. M.}, year={2024}, month={Sep.}, pages={60-76} }