All Questions

(I'm reposting here this question from MSE as it didn't receive any answer for two weeks.) Consider a sequence of finite lattices in $\mathbb{R}^n$ defined by $$L_k= [-k,k]^n \cap 2^{-k}\cdot \mathbb{...

This problem seems like it should be quite easy/standard, but I've not found a solution written down anywhere. Consider the set of 1-Lipschitz functions on the $[0,d]$ interval. Define the linear ...

Let $\lambda:[0, 1]\to \mathbb{R}$, and $b_{1j}, b_{2j}:[0, 1] \to \mathbb{R}$, $j = 1, \ldots, m$ be smooth functions. Consider the following two sets $$\begin{align*} S_1 &= \left\{ \begin{...

Let $V$ be a compactly-supported vector field on $\mathbb{R}^2$, whose zeros inside some open neighbourhood of the closed unit disk $\mathbb{D}^2$ are isolated. Does there exist a sequence of ...

Let $\Omega$ be a sufficiently regular domain, for example $\Omega=B(0,r)$, $r>0$, and $m(x)=\textrm{dist}(x,\partial \Omega)$ be the distance to boundary function. Suppose $\mathcal{F}$ is a ...

Let $\Omega \subseteq \mathbb{R}^n$ be an open bounded domain with a smooth boundary. Fix $1<p<n$. Let $A \in W^{1,p}(\Omega;\text{End}(\mathbb{R}^n)) \cap C(\Omega;\text{End}(\mathbb{R}^n))$ ...