Linked Questions

Let $u$ be a function such that $|u|^{(p-2)/2}u$ is in $H^1_0(G)$, $G$ is open and $p>2$. How can I show that $$ D(|u|^{(p-2)/2}u)=p/2|u|^{(p-2)/2}D(u) \label{1}\tag{1} $$ or how can I show that, ...

Let us define the density of subset $A\subset\omega$ : $$\rho(A)=\lim_{n\to\infty}\frac{|A\cap n|}{n}$$ if the limit exists. Let $\mathcal{F_1}=\{A\subset\omega~|~\rho(A)=1\}$. $\mathcal{F_1}$ is the ...

There is a folklore conjecture that $\operatorname{Ext}^2$ vanishes in the category of geometric $p$-adic Galois representations (i.e. representations that are unramified almost everywhere and de Rham ...

I was always thinking, in an informal way, that the powerset lattices ${\cal P}(X)$ (where $X$ is an infinite set) are the "widest" bounded distributive lattices with respect to their height. (In ${\...

I am looking for a list of mathematical technicalities that are not so well-known, even in the mathematical community. What I mean is, I am looking for examples of phenomenon where it is important to ...

Here, Martin Brandenburg says it is not true that "Every short exact sequence of the form $0 \to A \to A \oplus B \to B \to 0$ splits." Then Mohan says in comments that "As a positive result, If $0 ...

In the survey paper Poset Topology: Tools and Applications by Michelle Wachs, there is the following theorem on p46: Theorem 3.2.4 (Björner and Wachs [40]). Suppose $P$ is a poset for which $\...

I am looking for an example of a topological group $G$ acting by homeomorphisms on a metrizable space $X$ such that the orbit map $X\to X/G$ doesn't have the path lifting property, that is, there is a ...