 Poincare-Wirtinger inequality

ID: poincare-wirtinger-inequality

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

U

, every

u \in H^{1} (U)

satisfies

∥ u - u_{U} ∥_{L^{2} (U)} \leq C ∥\nabla u ∥_{L^{2} (U)}, u_{U} = \frac{1}{∣ U ∣} \int_{U} u .

Equivalently, the gradient norm is equivalent to the

H^{1}

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