5 problems

Let $\boldsymbol b$ satisfy assumptions $(b1)$–$(b4)$, let $u\in BV(\Omega)\cap L^\infty(\Omega)$, and let $(\boldsymbol b(\cdot,u),Du)_V$ denote the pairing measure introduced in…

Let $f\colon {\mathbb{R}}^n\times {\mathcal{S}}^{n-1}\to [0,\infty)$ be an even function. We say that $f$ is ${\rm BV}$-elliptic with respect to ${\rm PC}_0$ if, for every…

The spaces $BV^q$ and $BV$ are being compared through their jump variations: for $u\in BV(\mathbb{R}^N,\mathbb{R}^d)$, the jump part of its distributional derivative has total vari…

Let $\mathbb G$ be a Carnot group. Property $\mathscr R$ means that, for every bounded open set $\Omega\subset\mathbb G$ and every $u\in BV_H(\Omega)$, the distributional…

Let $\Omega$ be the domain, let $\nu \in \mathbf{GY}(\Omega;\mathbb{R}^m)$ be a gradient Young measure, and let $v \in \operatorname{BV}(\Omega;\mathbb{R}^m)$. Write $\lambda_\nu$…