Geodesic
The Poisson problem in a~domain with a~cut
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 189-205

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {Yu. N. Subbotin and N. I. Chernykh},
     title = {The {Poisson} problem in a~domain with a~cut},
     journal = {Matemati\v{c}eskie trudy},
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Yu. N. Subbotin; N. I. Chernykh. The Poisson problem in a~domain with a~cut. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 189-205. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a8/