APDE Seminar @BCAM: Self-improving Poincaré-Sobolev type functionals in product spaces

Abstract

We give a geometric condition which ensures that (q, p)-Poincaré-Sobolev inequalities are implied from generalized (1,1)-Poincaré inequalities related to $L^1$ norms in the context of product spaces. We provide several (1,1)-Poincaré type inequalities adapted to different geometries and then show that our self-improving method can be applied to obtain special interesting Poincaré-Sobolev estimates.

The results are based on joint work with E. Cejas (UNL, Argentina), C. Pérez (BCAM) and, E. Rela (UBA, Argentina).