The isoperimetric problem for a class of non-radial weights and applications.

We study a class of isoperimetric problems on R + N where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type | x | k x N α. Our results imply some sharp functional inequalities, like for instance, Caffarelli-Kohn-Nirenberg type inequalities. [ABSTRACT FROM AUTHOR]