7 problems

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…

For $x^*\in\Omega\setminus\Sigma$, consider the blow-ups $v^{x^*,r}\in S^\infty(Q)$ of $v=\nabla u$ defined by … For $\mathcal{H}^1$-almost every $x^*\in\Omega\setminus\Sigma$, com…

Orsina–De Lellis conjecture. $\mathcal H^1$-almost every point $x$ satisfying $\nu(B_r(x))/r\to0$ as $r\to0^+$ is a Lebesgue point of $m$. This means that there exists $m(x)$ such…

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

Let $[...].$

Let $[...].$

Let $\varphi$ be a solution of the eikonal equation … and consider the Aviles–Giga functional … The associated entropy production is the relevant quantity for weak solutions of the…