Neumann Laplacian on a domain with tangential components in the boundary

Sergeï A. Nazarov (1) , Jan Sokolowski (2) , Jari Taskinen (3)

1 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
2 IECN - Institut Élie Cartan de Nancy
3 Helsingin yliopisto = Helsingfors universitet = University of Helsinki

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.

Mots clés: asymptotic analysis; Neumann Laplacian

Domaines: Equations aux dérivées partielles [math.AP]

Sergeï A. Nazarov, Jan Sokolowski, Jari Taskinen. Neumann Laplacian on a domain with tangential components in the boundary. 2008. ⟨hal-00204501⟩