Topics:
The aim of this course is an introduction to the analysis of variational problems depending on a parameter. Such problems appear in different ways, and the parameter may be constitutive, may represent the scale of a geometric inhomogeneity, a range of interaction, may be a coefficient of a perturbative term, etc. It may have different effects, favoring oscillations, concentration, topological singularities, dimension-reduction, etc., sometimes a combination of these. Our scope is recognize of what kind is the asymptotic effect of the parameter and give a series of ways to describe this effect in the spirit of the direct methods of the Calculus of Variations. To that end we will apply our analysis to a series of prototypical problems: homogenization, relaxed Dirichlet problems, theories of thin objects, phase transitions, interfacial problems, free-discontinuity problems, Ginzburg-Landau vortices, discrete approximations, non-local interactions, etc. The course is reasonably self-contained, and the level of prerequisites (elementary Calculus of Variations, Sobolev Spaces, Functional Analysis) will depend on the audience.
References:
Lecture notes are available at the following link (click)
Comunication:
The lecture of Nov 14th is cancelled to allow students to partecipate to the orientation day.
The Lecture of Nov 17th is posponed to Nov 24, room 133, 14:00-16:00 to avoid the superposition with other lectures
The Lecture of Nov 21th is posponed to Nov 21, room 133, 15:00-17:00
The lecture of Nov 28th is cancelled.