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Boundary problems constitute an essential field of common mathematical interest. The intention of this volume is to highlight several analytic and geometric aspects of boundary problems with special emphasis on their interplay. It includes surveys on classical topics presented from a modern perspective as well as reports on current research.
The collection splits into two related groups:
- analysis and geometry of geometric operators and their index theory
- elliptic theory of boundary value problems and the Shapiro-Lopatinsky condition
List of contents
I Rarefied Gases.- 1. Macroscopic limits of the Boltzmann equation: a review.- 2. Moment equations for charged particles: global existence results.- 3. Monte-Carlo methods for the Boltzmann equation.- 4. Accurate numerical methods for the Boltzmann equation.- 5. Finite-difference methods for the Boltzmann equation for binary gas mixtures.- II Applications.- 6. Plasma kinetic models: the Fokker-Planck-Landau equation.- 7. On multipole approximations of the Fokker-Planck-Landau operator.- 8. Traffic flow: models and numerics.- 9. Modelling and numerical methods for granular gases.- 10. Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation.- 11. On coalescence equations and related models.
Summary
Boundary problems lie in the center of research activities both in analysis and geometry. The book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.
