Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs

Kirill D. Cherednichenko; Yulia Yu. Ershova; Alexander V. Kiselev

Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs

Analysis of PDEs 2024-04-09 v4 Spectral Theory

Authors: Kirill D. Cherednichenko , Yulia Yu. Ershova , Alexander V. Kiselev

Abstract

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.

Keywords

neumann laplacian norm-resolvent convergence thin domains metric graphs resonant case vertex matching conditions error estimate

Cite

@article{arxiv.2205.04397,
  title  = {Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs},
  author = {Kirill D. Cherednichenko and Yulia Yu. Ershova and Alexander V. Kiselev},
  journal= {arXiv preprint arXiv:2205.04397},
  year   = {2024}
}

Comments

2 figures; continuation of arXiv 1808.03961; as accepted in Mathematics

Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs

Abstract

Keywords

Cite

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