5 problems

Meyers' conjecture. Up to determining the optimal value of $c$, the optimal constant is conjectured to be $c=2$.

Let $n\geq 3$ and $K>1$. A $K$-quasiregular mapping has higher integrability exponent $p(n,K)$, meaning that its derivative belongs locally to $W^{1,pn}$ for every exponent below t…

For a domain in $\mathbb{R}^n$, let $p_O^{{\scriptstyle{RH}}}(n,K)$ and $p_O^{{\scriptstyle{Sob}}}(n,K)$ denote the reverse Hölder and Sobolev higher integrability exponents associ…

The elliptic-cone higher-integrability conjecture. If

Let $n$ be the dimension and $K$ the distortion of a quasiregular mapping. Its sharp higher-integrability exponent is denoted by $p(n,K)$, meaning the largest exponent for which th…