4 problems

Kohn–Müller branching conjecture. The minimizers of the Kohn–Müller functional exhibit this branching structure.

Conti–Ortiz relaxation conjecture. As $\varepsilon\to0$, minimizers $u^\varepsilon$ of $\overline W^\varepsilon$ converge to solutions of

Finite-element locality conjecture. Minimizing $W_{\mathrm{magic}}^+$ in a finite element space fails to find microstructure.

Let $\Omega_j$, $j=1,\ldots,N$, be grains in $\mathbb{R}^3$ whose closures are topological manifolds with boundary, and let $T$ be the set of triple points. Suppose that the grains…