Il prof Nikolas Papageorgiou terrà il seguente minicorso di due giorni rivolto agli studenti della Laurea Magistrale in Matematica e del Dottorato in Matematica e Informatica:
VARIATIONAL AND MORSE THEORETIC TECHNIQUES FOR NONLINEAR PDE’S
- martedì 9 dalle 16 alle 18 aula B
- giovedì 11 dalle 16 alle 18 aula D
In these lectures we will first develop the basic ideas and results related to the variational approach to boundary value problems. In this direction we will discuss the critical point theory for smooth functionals and the minimax characterization of the critical values. This analysis will also lead us to some fundamental variational principles such as the Ekeland variational principle. We will also mention multiplicity results based on symmetry properties of the energy functional.
Then we will pass to Morse theory. Based on an axiomatic approach to homology theory, we will introduce the notion of critical groups for an isolated critical point. We will see how we can compute the critical groups for some particular critical points. Critical groups allow us to prove multiplicity theorems and to distinguish between solutions.
Concrete examples from semilinear boundary value problems will be presented.