- The student is able to apply the reasoning of Calculus of Variations to concrete problems.
- The student knows necessary and sufficient conditions for the existence of minimizers of functionals arising in variational problems.
- The student is familiar with Sobolev Spaces and knows basic properties and embedding theorems.
- The student can derive the Euler-Lagrange equations.
Calculus of variations is a classical field in analysis and plays an important role in both, pure and applied mathematics. It is interconnected with other branches in mathematics, such as PDEs, geometry and optimal control, and has various applications in physics and engineering, e.g., in classical mechanics, quantum mechanics, material science and image processing.
The Calculus of Variations deals with optimization problems. Typically, one aims to find and analyze functions (within an appropriate class) that minimize or maximize a certain functional.
This course gives an introduction to the field and addresses classical problems, results and techniques.