Variational Problems¶on Multiply Connected Thin Strips I:¶Basic Estimates and Convergence¶of the Laplacian Spectrum

By J. Rubinstein, M. Schatzman. 2001

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Geometrical Structure of Laplacian Eigenfunctions (2012, background): “Kosugi studied the convergence of the solution to a semilinear elliptic equation in a thin network-shaped domain which degenerates into a geometric graph when a certain parameter tends to zero [288] (see also [295, 408, 431, 432]).”
On the spectrum of the Dirichlet Laplacian in a narrow strip (2007, background): “Rubinstein and Schatzman studied in [10] eigenvalues of the Neumann Laplacian in a narrow strip surrounding an embedded planar graph.”
Nonclassical Sturm-Liouville problems and Schrodinger operators on radial trees (2000, background): “More recently there have been mathematical studies, some concerned with the interpretation of differential operators on graphs as limits of partial differential operators on thin domains [10, 12, 18, 33, 35], while others focus on novel problems of spectral or scattering theory [4, 5, 6, 14, 23].”