On weighted second order Adams inequalities with Navier boundary conditions

Abstract

We obtain some sharp weighted version of Adams' inequality on second order Sobolev spaces with Navier boundary conditions. The weights that we consider determine a supercritical exponential growth, except in the origin, and the corresponding inequalities hold on radial functions only. We also consider the problem of extremal functions, and we show that the sharp suprema are achieved, as in the unweighted classical case.