We consider a class of isoperimetric problems on $\mathbb{ R}^{ N}_{ +} $ where the volume and the area element carry two different weights of the type $|x|^lx_N^\alpha$. We solve them in a special case while a more detailed study is contained in \cite{ ABCMP2}. Our results imply a weighted Polya-Sz\"ego principle and a priori estimates for weak solutions to a class of boundary value problems for degenerate elliptic equations
Categories: math.AP