1. A STRANGE VERTEX CONDITION COMING FROM NOWHERE.
- Author
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RÖSLER, FRANK
- Subjects
- *
NEUMANN problem , *QUANTUM graph theory , *SPECTRAL theory , *RESOLVENTS (Mathematics) - Abstract
We prove norm-resolvent and spectral convergence in L² of solutions to the Neumann Poisson problem --Δε= f on a domain Ωε perforated by Dirichlet holes and shrinking to a 1- dimensional interval. The limit u satisfies an equation of the type --u" + μu = f on the interval (0, 1), where μ is a positive constant. As an application we study the convergence of solutions in perforated graph-like domains. We show that if the scaling between the edge neighborhood and the vertex neighborhood is chosen correctly, the constant μ will appear in the vertex condition of the limit problem. In particular, this implies that the spectrum of the resulting quantum graph is altered in a controlled way by the perforation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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