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Martin Sleziak
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Hausdorff dimension of the zero set of $\nabla f$

Let $f: \mathbb R^n \to \mathbb R$ be a Lipschitz function with $\nabla f$ nonzero almost everywhere with respect to Lebesgue measure.

What is the supremal Hausdorff dimension of the set on which $f$ is differentiable with $\nabla f = 0$?