Explicit solution of the jump problem for the Laplace equation and singularities at the edges (Q5933551)

The explicit solution of the following problem is given: Let \(\Gamma_1,\dots ,\Gamma_n \) be smooth curves, \(f_1\), \(f_2\) be given functions on \(\Gamma =\Gamma_1 \cup \dots \cup \Gamma_n \). Find a function \(u\) harmonic in \(\mathbb{R}^2\setminus \Gamma \), such that the jump of \(u\) on \(\Gamma \) is equal to \(f_1\) and the jump of the normal derivative of \(u\) on \(\Gamma \) is equal to \(f_2\).