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
French Team
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
  1. 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.