Gaussian log-Sobolev inequality $\mathrm{Ent}_\gamma(f)\le\frac12\int (f')^2/f\,d\gamma$ for $C^1$ functions $f$ bounded away from $0$ with bounded derivative

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Gaussian log-Sobolev inequality $\mathrm{Ent}_\gamma(f)\le\frac12\int (f')^2/f\,d\gamma$ for $C^1$ functions $f$ bounded away from $0$ with bounded derivative · Prove2Me