6 problems

Let $d\geq 2$, let $\nu_{x,y}(\xi)$ be a Young-measure density analytic in $x$ and $y$, discretize $\xi$ algebraically at $N_\xi\sim\varepsilon^{-1}$, and suppose $R_1$ is polynomi…

Let the proposed notion be the notion introduced in the paper for nonlocal vector fields and their associated gradient Young measures. For $1\leq p<\infty$, consider approximation…

Let $z^\varepsilon:\mathbb{R}^m\to\mathbb{R}^N$ be weakly convergent and subject to linear differential constraints … where each $A_j$ is an $s\times N$ constant matrix, and to the…

Let $\Omega$ be the underlying domain, let $Z$ be the second-scale space, and let $\mathcal A$ be the differential constraint defining $\mathcal A$-free two-scale Young measures. L…

Strong Young measure solution conjecture. Under the variationally hyperbolic condition, the flow of the system always generates a strong Young measure solution; equivalently,

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 $\lambda_\nu$…