- Lecture 1: Intro and Classification
- Lecture 2: Motivation and Examples
- Lecture 3 & 4: Spherical Harmonics
- Lecture 5: Fourier Transform I
- Lecture 6 & 7: Fourier Transform II
- Lecture 8 & 9: Laplace Equation
- Lecture 10: Green’s Representation I
- Lecture 11: Green’s Representation II
- Lecture 12: Poisson Equation and Schauder Estimates
- Lecture 13: Schauder Estimates
- Lecture 14: Weak Derivatives
- Lecture 15: Sobolev Spaces
- Lecture 16: Imbedding Results
- Lecture 17: Compactness Results
- Lecture 18: Extension Results
- Lecture 19: Trace Results I
- Lecture 20: Potential Estimates
- Lecture 21: Application of Potential Estimates to Imbedding Results
- Lecture 22: Weak Solutions and Differentiability
- Lecture 23a: Introduction to Calculus of Variations
- Lecture 23b: Existence via Direct Methods
- Lecture 24: Trace Results II
- Lecture 25: Regularity Results
- Lecture 26: Existence via Hilbert Space Methods
- Lecture 27: Spectral Theory for Elliptic Operators
- Lecture 28: Spectral Theory Example for Vibrating Membrane
Paris Lodron Universität Salzburg
Kapitelgasse 4-6
5020 Salzburg, Austria
T +43 662 8044-0
F +43 662 8044-145
