Does the squared root belong $\sqrt{|\cdot|}$ to $BV((-1,1))$? In an affirmative case, what is its derivative in the distributional sense, i.e., what is the Radon measure $\mu$ such that $\mu=Du$ ?
2026-03-27 23:13:00.1774653180
Does the squared root $\sqrt{|\cdot|}$ belong to $BV((-1,1))$?
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Both of your questions are answered by the following identity: $$\sqrt{|x|}= 1+\frac12\int_{-1}^x |t|^{-1/2} \operatorname{sign} t \,dt$$