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Jun 23, 2020 at 14:22 vote accept T. Le
Jun 23, 2020 at 11:11 history became hot network question
Jun 23, 2020 at 4:49 answer added Piero D'Ancona timeline score: 8
Jun 23, 2020 at 4:49 comment added Daniele Tampieri I think the answer is no even in higher dimension, since the gradient of any characteristic function $\chi_\Omega$, $\Omega\Subset\Bbb R^n$ as exactly the same properties of $D=d/dx$, i.e. $\nabla \chi_\Omega\subseteq\partial\Omega$ as it is shown in this Q&A. And if you need a single PDE satisfying this property, you can take the divergence of the gradient and form the laplacian of the characteristic function.
Jun 23, 2020 at 3:18 history edited T. Le CC BY-SA 4.0
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Jun 23, 2020 at 3:09 history asked T. Le CC BY-SA 4.0