Sobolev spaces of symmetric functions and applications

We prove sharp pointwise estimates for functions in the Sobolev spaces of radial functions defined in a ball. As a consequence, we obtain some imbeddings of such Sobolev spaces in weighted L q -spaces. We also prove similar imbeddings for Sobolev spaces of functions with partial symmetry. Our techni...

Full description

Saved in:
Bibliographic Details
Published in:Journal of functional analysis 2011-12, Vol.261 (12), p.3735-3770
Main Authors: Guedes de Figueiredo, Djairo, Moreira dos Santos, Ederson, Hiroshi Miyagaki, Olímpio
Format: Article
Language:English
Subjects:
Biharmonic equation
Hardy type inequalities
Hénon type weights
Non-standard Sobolev imbeddings
Sobolev spaces
Supercritical problems
Symmetric functions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove sharp pointwise estimates for functions in the Sobolev spaces of radial functions defined in a ball. As a consequence, we obtain some imbeddings of such Sobolev spaces in weighted L q -spaces. We also prove similar imbeddings for Sobolev spaces of functions with partial symmetry. Our techniques lead to new Hardy type inequalities. It is important to observe that we do not require any vanishing condition on the boundary to obtain all our estimates. We apply these imbeddings to obtain radial solutions and partially symmetric solutions for a biharmonic equation of the Hénon type under both Dirichlet and Navier boundary conditions. The delicate question of the regularity of these solutions is also established.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2011.08.016