6 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 $\Omega\subset\mathbb{R}^2$ and let $u\in BV(\Omega;\mathbb{R}^m)$ belong to a suitable class of maps of bounded variation. For open sets $A\subset\Omega$, consider the strictl…

Let $(P)$ be the nonconvex sweeping control problem considered in the paper, with standing assumptions (H1)--(H5), except that the lower semicontinuity of the functions $\varphi$ a…

Let $I(y,\{s_j\},\lambda)$ be the laminated energy for a Lipschitz weight $\lambda\in\mathrm{Lip}(\Omega)$ satisfying $0<\lambda(x)<1$, and define … Here the slips $s_j$ are assume…

Let $E_{\mathrm{lb}}$ denote the lower-bound energy and let $E_{\mathrm{ub}}^{(1)}$ be the upper bound obtained from laminates with plane-wise constant weights. In the setting wher…

Ambrosio–De Lellis–Mantegazza conjecture. If $f(t)=t^p$ with $1\leq p\leq3$, then $\overline{\mathcal{I}_f}$ is lower semicontinuous for the strong topology in $L^1$.