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 ...

We consider boundary integral equations of the first kind with logarithmic kernels on smooth closed or open contours in R2. Instead of solving the first kind equations directly, we propose a fully ...