This article is cited in 7 scientific papers (total in 7 papers)
On estimate of eigenfunctions of the Steklov-type problem with a small parameter in the case of a limit spectrum degeneration
V. A. Sadovnichiia, A. G. Chechkinab
a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
b The State Uneversity of the Ministry of Finance of the Russian Federation, Moscow, Russia
We consider a Steklov-type problem with rapidly alternating boundary conditions (Dirichlet and Steklov) in a bounded two-dimensional domain. The parts of the boundary, where the Dirichlet boundary condition are given, have the length of the order $\varepsilon$ and they alternate with parts of the length of the same order, having the Steklov condition. We prove that the normalized eigenfunctions for a sufficiently small $\varepsilon$ satisfy the Friedrichs-type inequality with the constant of the order $\varepsilon$ and moreover, they converge to zero as $\varepsilon$ tends to zero.
spectrum of operator, Steklov-type problem, homogenization, asymptotics.
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V. A. Sadovnichii, A. G. Chechkina, “On estimate of eigenfunctions of the Steklov-type problem with a small parameter in the case of a limit spectrum degeneration”, Ufimsk. Mat. Zh., 3:3 (2011), 127–139
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\by V.~A.~Sadovnichii, A.~G.~Chechkina
\paper On estimate of eigenfunctions of the Steklov-type problem with a~small parameter in the case of a~limit spectrum degeneration
\jour Ufimsk. Mat. Zh.
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