Scientific co-operation project Austria-France 2017 - 2018
Spectral analysis of boundary value problems
The project FR 01/2017 is a cooperation of the institute of applied mathematics of the TU Graz and the Departement de Mathematiques d’Orsay of the Universite Paris Sud. It is funded by the Austrian Agency for International Cooperation in Education and Research (OeAD-GmbH) and the The French national agency for the promotion of higher education, international student services, and international mobility.
Project Team
Austrian Team
Univ.-Prof. Dr. Jussi Behrndt (supervision) Dipl. Ing. Markus Holzmann Simon Stadler
French Team
MCF HDR Konstantin Pankrashkin (supervision) Dr. Thomas Ourmieres-Bonafos Magda Khalile MCF Nicolas Popoff
Motivation and project description
The aim of this project is to develop new approaches to the spectral analysis of several classes of partial differential operators with suitable boundary conditions. The spectral theory of differential operators represents one of the central and most important topics in modern mathematical physics. For example, the analysis and computation of the spectrum of a given differential operator is a key point for questions concerning the propagation of waves, and various spectral problems appear as a linearization of suitable functionals and play a key role in the study of variational problems or in the justification of numerical methods. In the project we are particularly interested in the connection of the spectral properties and boundary or interface conditions.
Main problems, which will be considered during the project
Robin problems in polygonal and polyhedral domains Schrödinger operators with singular interactions supported by non-smooth hypersurfaces Dirac operators with δ-potentials
Visits in 2017
Thomas Ourmieres-Bonafos, Graz, 27 March - 31 March Magda Khalile, Graz, 23 April - 28 April Markus Holzmann, Orsay, 28 May - 9 June Konstantin Pankrashkin, Graz, 3 July - 7 July Nicolas Popoff, Graz, 20 November - 24 November Jussi Behrndt, Orsay, 26 November - 1 December Markus Holzmann, Orsay, 26 November - 2 December
Related publications
M. Holzmann, T. Ourmieres-Bonafos, and K. Pankrashkin, Dirac operators with Lorentz scalar shell interactions, arXiv.
Related events
There is an initial workshop in the week 24 April - 28 April.