 Hardy inequality in Euclidean space

ID: hardy-inequality-in-euclidean-space

For

d \geq 3

and

u \in H^{1} (R^{d})

\int_{R^{d}} \frac{∣ u ( x ) ∣ ^{2}}{∣ x ∣ ^{2}} d x \leq \frac{4}{( d - 2 ) ^{2}} \int_{R^{d}} ∣\nabla u (x) ∣^{2} d x .

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