Non compact variational problems

The purpose of the course is to illustrate a group of

variational problems that exhibit lack of compactness,

and to show general and more specific techniques that

allow them to be addressed. The difficulties of these

problems are due to the lack of compactness of

embedding for appropriate function spaces, originating

from geometric properties of invariance by

rescaling (conformal curvature prescription).

Techniques such as the use of symmetric spaces, the

principle of compactness by concentration, and the use of

asymptotic or perturbative estimates to make up for the

problem of lack of compactness will be discussed.