PDE2 - Nonlinear Partial Differential Equations

What it is about

You learn methods for existence and qualitative analysis of nonlinear partial differential equations. The focus is on variational techniques (calculus of variations, Euler–Lagrange, existence of minimizers, regularity) as well as nonvariational methods (monotone, fixed-point iterations, sub- and supersolutions, methods for proving non-existence). In the end you can apply these tools to semilinear elliptic problems.

What you will be able to do

• Applying the first and second variation and deriving the Euler–Lagrange equation
• Assessing the existence of minimizers via coercivity, boundedness from below and convexity
• Construction and analysis of weak solutions and investigation of their regularity
• Applying critical point theory (e.g. Mountain-Pass) to semilinear elliptic PDEs
• Use of nonvariational techniques: monotone, fixed-point methods as well as sub-/supersolutions
• Assessing methods for proving the non-existence of solutions

What the module consists of

• VorlesungTransmission of theoretical content, examples and discussion
• Übung/PraktikumWorking on concrete examples and problems for deeper understanding under supervision

Teaching method

• Lecture with examplesPresentation of the content and stimulation for independent analysis
• Discussion with studentsInvolving students for deepening and understanding check
• ÜbungsstundenPractical application and independent verification of learning success