All Questions

Let $\Omega\subset \Bbb R^d$ be open. The space $BV(\Omega)$ consists in functions $u\in L^1(\Omega)$ with bounded variation, i.e. $|u|_{BV(\Omega) }<\infty$ where \begin{align}\label{eq:bounded-...

Let $\Omega$ be a bounded domain in $\Bbb R^n$. Define $$ \Omega_r=\{x\in\Omega: \text{dist}(x,\partial\Omega)<r \}, $$ i.e. it the ring of thickness $r$ at the boundary of $\Omega$. Intuitively, ...

Given a Riemannian manifold $M$, we say $f: M \to \mathbb R$ is a strict contraction if $|f(x) - f(y)| < |x - y|$ for all distinct $x, y \in M$. Question: Does there exist, on every complete ...

It is well know that there is a generalization of Lebesgue decomposition theorem in the following way: Any non negative Radon measure can be decomposed uniquely into the sum of an absolutely ...

By Alberti rank-one theorem, could it be possible to reduce the study of a function $u \in BV(\mathbb{R}^N, \mathbb{R}^N)$ to the study of a function $\tilde{u} \in BV(\mathbb{R}^2, \mathbb{R}^2)$? At ...