Singularity of eigenfunctions at the junction of shrinking tubes, Part II

In continuation with [17], 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 [17]; most of all, we provide the exact asymptotic behavior of the implicit normalization for solutions given in [17] and thus describe the (N−1)(N−1)-order singularity developed at a junction of the tube (where N is the space dimension).