6 problems

Geometric lower-semicontinuity conjecture. A geometric condition on $\omega(u_0;r)$ could be used to improve the Hölder exponent in the estimate for the displacement of the iterate…

Let $Y$ be a normal $\mathbb{Q}$-Gorenstein variety and let $\mathfrak{a}$ be a non-zero $\mathbb{R}$-ideal sheaf on $Y$. LSC conjecture. The function … is lower semi-continuous, w…

Let $\varphi: Y \to T$ be a flat morphism, let $\mathfrak{a}$ be an $\mathbb{R}$-ideal sheaf on $Y$, and let $\tau: T \to Y$ be a section of $\varphi$. For a closed point $t \in T$…

Let $\Omega\subset\mathbb R^N$ be the domain, let $W$ be the integrand in … and suppose that $W(x,y,\cdot,\cdot)$ is separately curl Young quasiconvex. The local functional has the…

Ignat–Merlet conjecture. Then $(\nabla\varphi_0)^\perp$ is a global minimizer of $\mathcal{I}_f$.

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 $L^1$.