A boundary value problem for the~Laplacian with rapidly changing type of~boundary conditions in a~multidimensional domain
In the article under review, the authors study boundary value problems for the Laplacian in \(\mathbb R^n\), \(n\leq 3\), with rapidly changing boundary conditions. As in the case of \(n=2\) considered in [\textit{G. A. Chechkin}, Mat. Sb., 184, No. 6, 99-150 (1993; Zbl 0875.35009)], the explicit form of the limit problem depends on the asymptotic behavior of the first eigenvalue of the spectral problem for the Laplacian operator that is cellular. An essential part of the article is devoted to studying the indicated asymptotic behavior for \(n\geq 3\). The authors use the methods worked out by Oleĭnik.
rapidly changing type of boundary conditions
asymptotic behavior of the minimal eigenvalue
scientific article; zbMATH DE number 1432310