Critical Hardy--Sobolev Inequalities

Filippas, S.; Maz'ya, V.; Tertikas, A.

Critical Hardy--Sobolev Inequalities

Authors

Filippas, S.

Maz'ya, V.

Tertikas, A.

Description

We consider Hardy inequalities in $I R^n$, $n \geq 3$, with best constant that involve either distance to the boundary or distance to a surface of co-dimension $k<n$, and we show that they can still be improved by adding a multiple of a whole range of critical norms that at the extreme case become precisely the critical Sobolev norm.
22 pages