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

Kirill D. Cherednichenko, Yulia Yu. Ershova and Alexander V. Kiselev ()
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Kirill D. Cherednichenko: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
Yulia Yu. Ershova: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
Alexander V. Kiselev: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK

Mathematics, 2024, vol. 12, issue 8, 1-21

Abstract: Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in R d , 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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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