Gradient estimate for the heat flow: $\|\nabla e^{\nu t\Delta}f\|_2^2 \le \frac{24}{\nu t}\|f\|_2^2$

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Gradient estimate for the heat flow: $\|\nabla e^{\nu t\Delta}f\|_2^2 \le \frac{24}{\nu t}\|f\|_2^2$ · Prove2Me