Weighted Sobolev spaces of radially symmetric functions

Abstract

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.

38 pages

References in corpus (1)

• Radially symmetric solutions to the Hènon-Lane-Emden system on the critical hyperbola

Cited by in corpus (2)

• Symmetry breaking of extremals for the Caffarelli-Kohn-Nirenberg inequalities in a non-Hilbertian setting
• Sharp Sobolev and Adams-Trudinger-Moser inequalities for symmetric functions without boundary conditions on hyperbolic spaces