A collection of sharp dilation invariant inequalities for differentiable functions

Details A collection of sharp dilation invariant inequalities for differentiable functions A collection of sharp dilation invariant inequalities for differentiable functions

2008-02-21

arxiv.org/abs/0802.3209v2

Mathematics

Analysis of PDEs

revised and extended version

Scientific paper

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.

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