 Logarithmic Caccioppoli inequality

ID: logarithmic-caccioppoli-inequality

For a positive weak supersolution

u

of a uniformly elliptic divergence-form equation, testing with

η^{2} / u

gives

\int η^{2} ∣ D lo g u ∣^{2} \leq C \int ∣ Dη ∣^{2} .

The constant depends only on the ellipticity bounds.

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