All Questions

Let $\Omega\subset\Bbb R^d$ be an open set. Let $k:\Bbb R^d\to [0,\infty)$ be measurable such that $0\in \operatorname{supp}k$. This implies that $\Omega\subset \Omega_k=\Omega+\operatorname{supp}k$. ...

Let $C$ be a $C^1$ hypersurface in $R^n$ and let $u \in C^1(R^n)$. Suppose $$\nabla u(x) \cdot \eta(x)=|\nabla u| \ \ \forall x\in C$$ where $\eta(x)$ is the normal vector to $C$ at $x$ ($\nabla u$ ...