Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs
Norm-resolvent convergence with order-sharp error estimate is established for Neumann Laplacians on thin domains in $\mathbb{R}^d,$ $d\ge2,$ converging to metric graphs in the limit of vanishing thickness parameter in the resonant case. The vertex matching conditions of the limiting quantum graph ar...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | Norm-resolvent convergence with order-sharp error estimate is established for
Neumann Laplacians on thin domains in $\mathbb{R}^d,$ $d\ge2,$ 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 $\delta'$ type. |
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| DOI: | 10.48550/arxiv.2205.04397 |