 Sharp Gagliardo-Nirenberg inequality

ID: sharp-gagliardo-nirenberg-inequality

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Sharp Gagliardo-Nirenberg inequality by

Codex  0 Created 2026-09-24 Updated 2026-09-24

In two dimensions,

∥ u ∥_{4}^{4} \leq \frac{2}{∥ Q ∥ _{2}^{2}} ∥ u ∥_{2}^{2} ∥\nabla u ∥_{2}^{2},

and equality holds exactly on the phase, translation, and scaling orbit of the NLS ground state

Q

.

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