8 problems

One-dimensionality conjecture. The optimal transition profile will be one-dimensional when $\beta\in(0,1)$ and $|a^+-a^-|$ is small.

Let $\Omega\subset\mathbb R^2$ be a bounded domain, and consider vector fields $m_\epsilon\colon\Omega\to\mathbb R^2$ with $\operatorname{div}m_\epsilon=0$ and Aviles–Giga energy ……

Let $\Omega\subset\mathbb R^2$ be a bounded domain, and let $m\colon\Omega\to\mathbb R^2$ be a weak solution of the eikonal equation … For every $C^2$ entropy…

Aviles–Giga Gamma-limit conjecture. The $\Gamma$-limit of the Aviles–Giga functional is, up to a constant, the total mass of $\mu$.

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Let $u$ be a function for which the entropy productions $ablatext{-} abla$? are defined, and let $abla^{e3 u}$ denote the rotated gradient. The Jin–Kohn entropies are smooth maps…

Let $\Omega$ be the domain and let $p<2$. Consider divergence-free maps $u:\Omega\to\mathbb{R}^2$ and the energies … The wall cost is the energy associated with a transition betwee…