Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain
Giuseppe Cardone, С. А. Назаров, Jan Sokołowski, Jari Taskinen · Comptes Rendus Mécanique · 2007
We construct the asymptotics (as ε → 0 ) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε > 0 .