$f \in C^{1,1}( \bar \Omega)$ and $f > 0$ in $\Omega$ then $|\nabla f| \leq C \sqrt{f}$

by Weeson Dorne   Last Updated October 10, 2019 04:20 AM

Let $f \in C^{1,1}( \bar \Omega)$ and $f > 0$ in $\Omega$. How to show that $|\nabla f| \leq C \sqrt{f}$ ,wehre $C$ depends on $|f|_{C^{1,1}}$ and $\Omega$.

Tags : functions


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