In continuation with Part I, we investigate the asymptotic behavior of weighted eigenfunctions in two half-spaces connected by a thin tube. We provide several improvements about some convergences stated in Part I; most of all, we provide the exact asymptotic behavior of the implicit normalization for solutions given in Part I and thus describe the (N−1) -order singularity developed at a junction of the tube (where N is the space dimension)
Abatangelo, L., Felli, V., Terracini, S. (2014). Singularity of eigenfunctions at the junction of shrinking tubes, Part II. JOURNAL OF DIFFERENTIAL EQUATIONS, 256(10), 3301-3334 [10.1016/j.jde.2014.02.010].
Singularity of eigenfunctions at the junction of shrinking tubes, Part II
ABATANGELO, LAURA;FELLI, VERONICA;
2014
Abstract
In continuation with Part I, we investigate the asymptotic behavior of weighted eigenfunctions in two half-spaces connected by a thin tube. We provide several improvements about some convergences stated in Part I; most of all, we provide the exact asymptotic behavior of the implicit normalization for solutions given in Part I and thus describe the (N−1) -order singularity developed at a junction of the tube (where N is the space dimension)
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