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

Kirill Cherednichenko; Yulia Yu Ershova; Alexander V. Kiselev

doi:10.3390/math12081161

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

Kirill Cherednichenko, Yulia Yu Ershova, Alexander V. Kiselev

Texas A&M University

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

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Abstract

Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in (Formula presented.) (Formula presented.) 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 (Formula presented.) type.

Original language	English
Article number	1161
Journal	Mathematics
Volume	12
Issue number	8
DOIs	https://doi.org/10.3390/math12081161
Publication status	Published - 12 Apr 2024

Data Availability Statement

No new data were generated or analysed during this study.

Funding

K.D.C. and Y.Y.E. are grateful for the financial support of EPSRC Grant EP/L018802/2. KDC and AVK are grateful for the financial support of EPSRC Grant EP/V013025/1. Y.Y.E. and A.V.K. are grateful to IIMAS\u2013UNAM for the hospitality and financial support during the research visit when part of this work was carried out.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/L018802/2, EP/V013025/1

Keywords

PDE
generalised resolvent
norm-resolvent asymptotics
quantum graphs
thin structures

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

Access to Document

10.3390/math12081161Licence: CC BY

https://www.mdpi.com/2227-7390/12/8/1161Licence: CC BY

Cite this

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title = "Norm-Resolvent Convergence for Neumann Laplacians on Manifold Thinning to Graphs",

abstract = "Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in (Formula presented.) (Formula presented.) 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 (Formula presented.) type.",

keywords = "PDE, generalised resolvent, norm-resolvent asymptotics, quantum graphs, thin structures",

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AU - Kiselev, Alexander V.

PY - 2024/4/12

Y1 - 2024/4/12

N2 - Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in (Formula presented.) (Formula presented.) 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 (Formula presented.) type.

AB - Norm-resolvent convergence with an order-sharp error estimate is established for Neumann Laplacians on thin domains in (Formula presented.) (Formula presented.) 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 (Formula presented.) type.

KW - PDE

KW - generalised resolvent

KW - norm-resolvent asymptotics

KW - quantum graphs

KW - thin structures

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

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Quantitative tools for upscaling the micro-geometry of resonant media

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this

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

Abstract

Data Availability Statement

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Quantitative tools for upscaling the micro-geometry of resonant media

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this