Arbeitsgruppe Analysis und Partielle Differentialgleichungen
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.
Aktuelles
Cole Prize für Jessica Fintzen
Dr. Regula Krapf erhält Lehrpreis der Universität
Prof. Daniel Huybrechts erhält Compositio Prize für die Periode 2017-2019
Prof. Catharina Stroppel erhält Gottfried Wilhelm Leibniz-Preis 2023
Stipendien für Mathematikstudierende aus der Ukraine
Prof. Jessica Fintzen erhält einen Whitehead Prize der London Mathematical Society
Prof. Peter Scholze zum Foreign Member der Royal Society ernannt