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I think it is better to provide context in which the previous question Any formula or estimates the Green function for the Laplacian in $3D$ periodic box? has been raised. The motivation is the ...

Fix a polynomial mapping $\mathbb R^n\overset{f}{\to} \mathbb R$. This answer shows that if the top degree homogeneous component of $f$ is zero only at the origin, then $f$ is proper. Intuitively, ...

Let $\mathrm{\gamma} : [0,1] \to \mathbb{R}^2$ be a piecewise smooth, simple plane curve. Assume $\gamma(0) = (0,0)$, $\gamma(1) = (1,0)$ and that the slope of the tangent is not $0$ wherever it's ...

Let $U$ be an open, bounded and convex set in $\mathbb{R} ^n$. Since $\partial U$ is a rectifiable set it follows that up to a set of $H^{n-1}$-measure zero $\partial U$ is contained in a countable ...