First order operators on shrinking graph-like spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F25%3A00637959" target="_blank" >RIV/61389005:_____/25:00637959 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/25:00389375

Result on the web

<a href="https://iopscience.iop.org/article/10.1088/1751-8121/adeb1a" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/adeb1a</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/adeb1a" target="_blank" >10.1088/1751-8121/adeb1a</a>

Result language

angličtina

Original language name

First order operators on shrinking graph-like spaces

Original language description

In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the graph-like space, the first order operator is of the form exterior derivative (the gradient) on functions and its adjoint (the negative divergence) on closed 1-forms (irrotational vector fields). Under the assumption that each cross section of the tubular edge neighbourhood is convex, that each vertex neighbourhood is simply connected and under suitable uniformity assumptions (which hold in particular, if the space is compact) we establish generalised norm resolvent convergence of the first order operator on the graph-like space towards the one on the metric graph. The square of the first order operator is of Laplace type. On the metric graph, the function (0-form) component is the usual standard (Kirchhoff) Laplacian. A key ingredient in the proof is a uniform Gaffney estimate: such an estimate follows from an equality relating here the divergence operator with all (weak) partial derivatives and a curvature term, together with a (localised) Sobolev trace estimate.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

58

Issue of the periodical within the volume

30

Country of publishing house

GB - UNITED KINGDOM

Number of pages

31

Pages from-to

305202

UT code for WoS article

001536582600001

EID of the result in the Scopus database

2-s2.0-10511510039