7 problems

Let $r_n=2^{-n}$ and define the renormalized orbit … For a relative filter scale $\ell\in(0,1)$, let $F_{n,\ell}^{\rm abs}$ denote the absolute coarse flux activity, let…

Critical recurrence diagnostic conjecture. There exist relative filter scales $\ell_n\in[\ell_-,\ell_+]\subset(0,1)$, a subsequence, and a constant $c>0$ such that

Let $T$ be an optimal transport map between probability measures with compact supports, both absolutely continuous with respect to the Lebesgue measure with densities bounded from…

Let $v$ be the suitable weak solution and let $H(t,s)$ be the quantity defined by the iterated limits in the preceding existence theorem, for $t>s\geq 0$. The quantity $H(t,s)$ is…

Let $X_1,\ldots,X_N$ be smooth vector fields satisfying Hörmander's bracket-generating condition on a neighbourhood of a bounded domain, and let $\mathcal S_{min}$ be the set of al…

Let $S$ denote the set of singular points of a weak solution $({\mathbf{m}},p)$ in the biological network formulation model, and suppose $N=2$. Conjecture on two-dimensional regula…

Let $\lambda$ and $\Lambda$ be the ellipticity constants in Proposition 2.1, and let $\varepsilon$ denote the exponent in its $W^{2,\varepsilon}$ estimate. Optimal exponent conject…