RG Analysis and Partial Differential Equations
V5B7: Advanced Topics in Analysis - Sobolev Spaces
Winter Semester 2018/2019
- Dr. Olli Saari
- Instructor
Lectures
- Mo 12-14, 0.011
- Wed 12-14, 0.011
Topics
A preliminary selection- Review of real analysis,
- Lp spaces and duality
- Distributions
- Definition of Sobolev spaces
- Generalized Poincaré inequalities
- Poincaré's inequality
- Self-improving and local Sobolev embeddings
- Maximal functions measuring smoothness
- Hardy-Sobolev spaces
- Pointwise characterizations
- Interpolation
- Fractional order of smoothness and potentials
- Real and complex interpolation
- Besov and Triebel-Lizorkin scales
- Embeddings
- Fine properties
- Hausdorff measure
- Modulus and Capacity
- Precise representatives and absolute continuity
- Traces and extensions
- Some applications
Prerequisites
Lebesgue measure and integration, functional analysis (Banach spaces and operators), basic knowledge about the Fourier transformExam
The first exams take place on 28.2. and the other exam period is 27.3.-29.3.2019.Literature
- R.A. Adams, Sobolev spaces, 1975.
- Adams and Hedberg, Function Spaces and Potential Theory, 1999.
- Bergh and Löfström, Interpolation Spaces. An Introduction, 1976.
- A. and J. Björn, Nonlinear Potential Theory on Metric Spaces, 2011
- Evans and Gariepy, Measure Theory and Fine Properties of Functions, 1991.
- G. Leoni, A First Course in Sobolev spaces, 2009.
News
Angkana Rüland receives Gottfried Wilhelm Leibniz Prize 2025
Abel in Bonn: Abel Symposium 2025
Wolfgang Lück receives the von Staudt Prize
Gerd Faltings elected member of the Order Pour le Mérite
Geordie Williamson receives the Max Planck-Humboldt Research Award 2024
ERC Starting Grant for Markus Hausmann
EMS Prize 2024 for Jessica Fintzen
Bonn mathematics performs excellently again in QS ranking
Stefan Schwede is invited speaker at the ECM 2024 in Sevilla
Jessica Fintzen wins Cole Prize
Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Peter Scholze elected as Foreign Member of the Royal Society