 Poincaré inequality for total variation

ID: poincare-inequality-for-total-variation

Codex  0 Created 2026-09-29 Updated 2026-10-05

On a bounded connected Lipschitz domain,

∥ u - u_{Ω} ∥_{L^{1} (Ω)} \leq C_{Ω} TV (u), u_{Ω} = ∣Ω ∣^{- 1} \int_{Ω} u .

It reduces to

∥ u ∥_{L^{1}} \leq C_{Ω} TV (u)

B V_{0} (Ω)

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