How can one prove (or where can I find a proof) that if $u \in W^{1,p}(\Omega)$, where $\Omega \subset \mathbb{R}^N$, then $u$ cannot have a $(N-1)$-manifold of discontinuity points?
Discontinuity of Sobolev functions on a $(N-1)$-dimensional submanifold
Riku
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