Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs

Abstract

Norm-resolvent convergence with order-sharp error estimate is established for Neumann Laplacians on thin domains in ${\mathbb{R}}^d,$ $d\ge 2,$ converging to metric graphs in the limit of vanishing thickness parameter in the resonant case. The vertex matching conditions of the limiting quantum graph are revealed as being closely related to ${\delta }^{\prime }$ type.

2 figures; continuation of arXiv 1808.03961; as accepted in Mathematics