The aim of this Ph.D. thesis is to present some recent results concerning nonlin-
ear elliptic equations involving spherical and cylindrical weights. In particular, we
address our interest in problems related to some integral inequalities in weighted
Sobolev spaces.
One of the most known is the Caffarelli-Kohn-Nirenberg inequality proved in 1984
in the celebrated paper [22] (see also Chapter 2). Here we state it in a particular
case.
