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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
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