Seminari del Dipartimento di Matematica

Seminario del 2022

Federica Sani (Università di Modena e Reggio Emilia).

Extremal functions for Adams inequalities with Navier boundary conditions

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

We prove the existence of extremal functions for second order Adams inequalities with Navier boundary conditions on balls in R^n in any dimension n>3. The proof is based on a symmetrization argument and the ideas introduced by Carleson and Chang to prove the existence of extremal functions in the first order case, i.e. extremal functions for the Trudinger-Moser inequality on balls. We also derive a supercritical version of this result for spherically symmetric functions.