Nazarov, S. A. Asymptotic of the solution of the Neumann problem at a point of tangency of smooth components of the boundary of the domain. (English. Russian original) Zbl 0841.35030 Russ. Acad. Sci., Izv., Math. 44, No. 1, 91-118 (1995); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 1, 92-120 (1994). The author studies the asymptotics of the solution of a second-order elliptic equation in a region \(\Omega\) of \(\mathbb{R}^n\), in a situation in which there are two pieces of (smooth) boundary being tangent at some point. If \(n= 2\) then the solution of both the Dirichlet and the Neumann problem behaves exponentially near the tangency point, while if \(n> 2\), there is a complete asymptotic expansion. The results are too complicated to be stated here. Reviewer: A.Bove (Bologna) MSC: 35J25 Boundary value problems for second-order elliptic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:asymptotic expansion PDF BibTeX XML Cite \textit{S. A. Nazarov}, Russ. Acad. Sci., Izv., Math. 44, No. 1, 1 (1994; Zbl 0841.35030); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 58, No. 1, 92--120 (1994) Full Text: DOI