Page 474 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 474
CA18232: VARIATIONAL METHODS AND EQUATIONS ON GRAPHS (MS-40)
The talk is based on joint works with David Krejcˇiˇrík (Czech Technical University in Prague),
Petr Siegl (Queen’s University Belfast) and Delio Mugnolo (FernUniversität Hagen).
Spectral geometry of quantum graphs via surgery principles
James Kennedy, j.bernard.kennedy@gmail.com
University of Lisbon, Portugal
Coauthors: Gregory Berkolaiko, Pavel Kurasov, Delio Mugnolo
“Surgery" on a (metric) graph means making a small, generally local, change to its structure: for
example, joining two vertices, lengthening an edge, or maybe removing an edge and reinserting
it somewhere else.
We will introduce a number of sharp new surgery principles which allow one to control the
eigenvalues of the Laplacian on a metric graph with any of the usual vertex conditions (natural,
Dirichlet or delta). We will illustrate how these principles can be used to give new proofs
and sharper versions of existing “isoperimetric"-type eigenvalue estimates by sketching a result
which interpolates between the theorems of Nicaise and Band–Lévy for the first non-trivial
eigenvalue of the Laplacian with natural vertex conditions.
This is based on joint work with Gregory Berkolaiko, Pavel Kurasov and Delio Mugnolo.
Flows in infinite networks
Marjeta Kramar Fijavž, marjeta.kramar@fgg.uni-lj.si
University of Ljubljana, Slovenia
Coauthor: Christian Budde
We consider linear transport processes in infinite metric graphs in the L∞-setting. We apply
the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under
different assumptions on the velocities and for general stochastic matrices appearing in the
boundary conditions.
Semilinear evolution problems in fractal domains
Maria Rosaria Lancia, mariarosaria.lancia@uniroma1.it
Sapienza, Italy
Coauthor: Paola Vernole
We present some results on semilinear evolutions equations, possibly non autonomous , in frac-
tal domains.
Local existence, uniqueness and regularity results for the mild solution are proved.
472
The talk is based on joint works with David Krejcˇiˇrík (Czech Technical University in Prague),
Petr Siegl (Queen’s University Belfast) and Delio Mugnolo (FernUniversität Hagen).
Spectral geometry of quantum graphs via surgery principles
James Kennedy, j.bernard.kennedy@gmail.com
University of Lisbon, Portugal
Coauthors: Gregory Berkolaiko, Pavel Kurasov, Delio Mugnolo
“Surgery" on a (metric) graph means making a small, generally local, change to its structure: for
example, joining two vertices, lengthening an edge, or maybe removing an edge and reinserting
it somewhere else.
We will introduce a number of sharp new surgery principles which allow one to control the
eigenvalues of the Laplacian on a metric graph with any of the usual vertex conditions (natural,
Dirichlet or delta). We will illustrate how these principles can be used to give new proofs
and sharper versions of existing “isoperimetric"-type eigenvalue estimates by sketching a result
which interpolates between the theorems of Nicaise and Band–Lévy for the first non-trivial
eigenvalue of the Laplacian with natural vertex conditions.
This is based on joint work with Gregory Berkolaiko, Pavel Kurasov and Delio Mugnolo.
Flows in infinite networks
Marjeta Kramar Fijavž, marjeta.kramar@fgg.uni-lj.si
University of Ljubljana, Slovenia
Coauthor: Christian Budde
We consider linear transport processes in infinite metric graphs in the L∞-setting. We apply
the theory of bi-continuous operator semigroups to obtain well-posedness of the problem under
different assumptions on the velocities and for general stochastic matrices appearing in the
boundary conditions.
Semilinear evolution problems in fractal domains
Maria Rosaria Lancia, mariarosaria.lancia@uniroma1.it
Sapienza, Italy
Coauthor: Paola Vernole
We present some results on semilinear evolutions equations, possibly non autonomous , in frac-
tal domains.
Local existence, uniqueness and regularity results for the mild solution are proved.
472
