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Reading a paper, they use the fact that the function $x \mapsto \log |\det Df(x)|$ is $v$-Hölder, where $Df$ is the derivative of some map. Then, they state that the function $f$ is $C^{1+v}$ and continue the paper with this assumption. Does the condition of $f$ being $C^{1+v}$ imply the Hölder continuity of $\log|\det Df(x)|$?

Thanks

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    You might want to recall how $C^{1+v}$ regularity is defined (presumably for non integer $v$).2012-02-17

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