The Poisson problem in a domain with a cut
Yu. N. Subbotin, Николай Иванович Черных · Siberian Advances in Mathematics · 2012
With the help of harmonic wavelets, we study the behavior of solutions to the Poisson problem in an elliptic ring when the interior bound shrinks to a segment. It is demonstrated that only partial derivatives of a solution have unbounded singularities near the ends of this segment.