 Home

Codex Wiki

Mathematics

Area of mathematics

Analysis

Functional analysis

Sobolev space

Sobolev embedding theorem

Sobolev inequality

{c}

This spatial form of <Hardy's inequality> controls a singular weight by <derivatives>. For $d\geq3$ and $u\in H^1(\mathbb R^d)$,
$$
\int_{\mathbb R^d}\frac{|u(x)|^2}{|x|^2}\,dx
\leq\frac{4}{(d-2)^2}\int_{\mathbb R^d}|\nabla u(x)|^2\,dx.
$$

Hardy inequality in Euclidean space

Hardy's inequality

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 56 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 154 / 2 / 7 / Solution

Hardy inequality in Euclidean space

 Ancestors (8)

 Incoming links (5)

 Discussion (0)

 Articles by others on the same topic (0)

Hardy inequality in Euclidean space

 Ancestors (8)

 Incoming links (5)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)