$H^1$-seminorm contraction of the heat flow: $\|\nabla e^{\nu t\Delta}f\|_2 \le \|\nabla f\|_2$

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$H^1$-seminorm contraction of the heat flow: $\|\nabla e^{\nu t\Delta}f\|_2 \le \|\nabla f\|_2$ · Prove2Me