Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 34, 2009, 131-143
Russian Academy of Sciences, Institute of Problems of Mechanical Engineering
V.O., Bolshoi pr., 61, 199178, St. Petersburg, Russia; serna 'at' snark.ipme.ru
Université Henri Poincaré Nancy 1, Département de Mathematiques
B.P. n. 239, 54506 Vandoeuvre les Nancy Cédex, France;
Jan.Sokolowski 'at' iecn.u-nancy.fr
University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, 00014 Helsinki, Finland; Jari.Taskinen 'at' helsinki.fi
Abstract. We study the Neumann problem for the Poisson equation in a domain where two boundary components are tangential at a single point, such that a geometrical irregularity of the rotational cusp type is formed. We derive necessary and sufficient conditions for the existence of a solution with a finite Dirichlet integral.
2000 Mathematics Subject Classification: Primary 35J25; Secondary 46E35, 35J20.
Key words: Poisson equation, Neumann problem, nonsmooth boundary, rotational cusp.
Reference to this article: S.A. Nazarov, J. Sokolowski and J. Taskinen: Neumann Laplacian on a domain with tangential components in the boundary. Ann. Acad. Sci. Fenn. Math. 34 (2009), 131-143.
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