| Abstract: |
| We consider the problem of existence of extremal functions for second order Adams` inequalities with Navier boundary conditions on balls in $\mathbb R^n$ in any dimension $n \geq 4$. We also discuss some sharp weighted versions of Adams` inequality on the same spaces. The weights that we consider determine a supercritical exponential growth, except in the origin, and the corresponding inequalities hold for spherically symmetric functions only. |
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