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let $u$ be a p-harmonic function in $\Omega \subset \mathbb R^N$.

We already know that the set $\{u=0\}$ is locally a $C^{1,\alpha}$ hypersurface at the points where $\nabla u\neq 0$.

What can be said about the overall regularity of the set $\partial \{u\neq 0\}$. this will also include the points where gradient of u is zero.

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