Mathematics (Apr 2024)

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

  • Kirill D. Cherednichenko,
  • Yulia Yu. Ershova,
  • Alexander V. Kiselev

DOI
https://doi.org/10.3390/math12081161
Journal volume & issue
Vol. 12, no. 8
p. 1161

Abstract

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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