Communications in Analysis and Geometry
Volume 30 (2022)
Effective operators for changing sign Robin Laplacian in thin two- and three-dimensional curved waveguides
Pages: 1227 – 1268
We study the Laplacian in some thin curved domains, in the plane and space, with particular types of Robin boundary conditions and cross-sections. We derive, when the diameters of the cross sections tend to zero, nontrivial effective Schrödinger operators on the reference curve by means of norm resolvent convergences. Besides the changing sign in the Robin parameter, for which no renormalization is necessary, another novelty is that the torsion (in the spatial case) plays no role to effective operators.
Received 18 July 2016
Accepted 21 November 2019
Published 26 April 2023