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

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

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...

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Veröffentlicht in:Mathematics (Basel) 2024-04, Vol.12 (8), p.1161
Hauptverfasser: Cherednichenko, Kirill D., Ershova, Yulia Yu, Kiselev, Alexander V.
Format: Artikel
Sprache:eng
Schlagworte:
Convergence
Convergence (Mathematics)
generalised resolvent
Graph theory
Graphs
Hilbert space
Laplacian operator
Magnetic fields
Manifolds (Mathematics)
norm-resolvent asymptotics
PDE
Phase transitions
quantum graphs
Tests, problems and exercises
thin structures
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Beschreibung
Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12081161