The Dirichlet problem in a domain with a slit
Николай Иванович Черных, Yu. N. Subbotin · Proceedings of the Steklov Institute of Mathematics · 2009
A basis of harmonic wavelets is constructed in an elliptic ring, and its approximation properties are investigated. The results are used to analyze the behavior of a boundary-value Dirichlet problem under the contraction of the inner boundary of the ring to a segment.