In this course we discuss the theory of existence of solutions to non-linear elliptic PDEs via variational techniques. These reformulate the PDE at hand into the equation for the critical point of a suitable function on a Banach space. Using methods from Functional Analysis in combination with certain information on the topology of level sets one can show the existence of critical points. One interesting feature of this approac is that one can construct not only Energy minimizers, but also critical points, which are not extremal.
As prerequisites it is recommended that you completed an introductory course in PDE and Functional Analysis.
- Kursleiter:in: Jan Metzger