Modern aspects of Sobolev inequalities

This IHP summer school, consisting in a series of lectures by Andrea Cianchi and Jean Dolbeault, will cover modern techniques concerning the Sobolev and other related inequalities.  The first course will focus on reduction principles for Sobolev-type inequalities, based on symmetrization, isoperimetry, interpolation, and rearrangements. The second course will focus on carré du champ techniques, entropy methods and their application to extremal functions, symmetry, rigidity, and stability.