A collection of sharp dilation invariant inequalities for differentiable functions
Analysis of PDEs
2008-03-10 v2
Abstract
We find best constants in several dilation invariant integral inequalities involving derivatives of functions. Some of these inequalities are new and some were known without best constants. The contents: 1. Estimate for a quadratic form of the gradient, 2. Weighted G{\aa}rding inequality for the biharmonic operator, 3.Dilation invariant Hardy's inequality with remainder term, 4. Generalized Hardy-Sobolev inequality with sharp constant, 5. Hardy's inequality with sharp Sobolev remainder term.
Cite
@article{arxiv.0802.3209,
title = {A collection of sharp dilation invariant inequalities for differentiable functions},
author = {V. Maz'ya and T. Shaposhnikova},
journal= {arXiv preprint arXiv:0802.3209},
year = {2008}
}
Comments
revised and extended version