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{c}
{wiki=Hardy's_inequality}

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

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

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Hardy inequality in Euclidean space

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