The smoothness of the solution to a two-dimensional integral equation with logarithmic kernel
The author studies properties of the solution of the integral equation \[ u(x)=\int_ \Omega a(x,y)\ln | x-y | u(y) dy+f(x),\;x \in \Omega \] where \(\Omega \subset \mathbb{R}^ 2\) is an open bounded set with a piecewise Lyapunov boundary \(\partial \Omega\) and \(f\) and \(a\) are sufficiently smooth functions. She describes the leading singular parts of the derivatives of an arbitrary order of the solution depending on the smoothness properties of \(\partial \Omega\).
scientific article; zbMATH DE number 429273
scientific article