let $u\in W^{2,2}(\Omega,\mathbb{R}^n)$, $\Omega\subset \mathbb{R}^m$. Does the following inequality (estimation) make sense?
$$\bigg\vert D(\dfrac{\partial u}{\partial x_m})\bigg\vert\leq \vert D^2u\vert$$
let $u\in W^{2,2}(\Omega,\mathbb{R}^n)$, $\Omega\subset \mathbb{R}^m$. Does the following inequality (estimation) make sense?
$$\bigg\vert D(\dfrac{\partial u}{\partial x_m})\bigg\vert\leq \vert D^2u\vert$$
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