The existence-uniqueness of the solution and its behaviour for one-dimensional integral equations of the first kind with logarithmic kernels are investigated. The analysis is based on the transfinite ...

Consider solving the Dirichlet problem $$\Delta u(P) = 0, P \in \mathbb R^2\backslash S,$$ $$u(P) = h(P),\quad P \in S,$$ $$\sup|u(P)| < \infty,$$ $$P \in \Bbb{R}^2 ...