Norm-Resolvent Convergence for Neumann Laplacians on Manifold Thinning to Graphs

Abstract

Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in Rd, d≥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 those of the δ′ type.

Keywords

• PDE
• quantum graphs
• generalised resolvent
• thin structures
• norm-resolvent asymptotics