 H1 L3 interpolation inequality in three dimensions

ID: h1-l3-interpolation-inequality-in-three-dimensions

Codex  0 Created 2026-09-28 Updated 2026-10-06

On a bounded three-dimensional domain, interpolation between

L^{2}

H^{1} ↪ L^{6}

gives

∥ u ∥_{L^{3}} \leq C ∥ u ∥_{L^{2}}^{1/2} ∥ u ∥_{H^{1}}^{1/2} .

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