An Introduction to the Regularity Theory of Elliptic Partial Differential Equations

What it is about

You will get an introduction to the regularity theory of elliptic partial differential equations. You will learn classical and modern methods for deriving regularity results for linear and nonlinear problems as well as for systems, and you will be able to apply the most important proof techniques, e.g. De Giorgi's solution of Hilbert's XIX. In the end you will understand the basics of Nirenberg's methods, Schauder theory and partial regularity for systems.

What you will be able to do

• Understand the basic concepts and methods of the regularity theory of elliptic PDEs
• Apply the Nirenberg method
• Apply Schauder theory
• Understand partial regularity for systems
• Follow De Giorgi's solution of Hilbert's XIX
• Know the basics of viscosity solutions

What the module consists of

• VorlesungPresentation of the content in lectures with demonstrative examples and discussions; main teaching format

Teaching method

• Vortrag mit Beispielento present the concepts and proof methods
• Diskussionto deepen understanding and encourage students to engage in their own analysis
• Übungsaufgabento deepen and independently verify learning success