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I modified your question. I hope this is what you had in mind.
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Piotr Hajlasz
Piotr Hajlasz
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Can the derivative of a BV function $f:\mathbb{R}^n\to\mathbb{R}^n$ be controlled by itsthe symmetric part in any wayof the derivative $\frac{1}{2}(Df+(Df)^T)$?

Can the derivative of a BV function be controlled by its symmetric part in any way?

Can the derivative of a BV function $f:\mathbb{R}^n\to\mathbb{R}^n$ be controlled by the symmetric part of the derivative $\frac{1}{2}(Df+(Df)^T)$?

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Riku
Riku
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Control the derivative of a BV function by its symmetric part

Can the derivative of a BV function be controlled by its symmetric part in any way?