Iwaniec–Martin conjecture on weakly quasiregular mappings

Let $cuOmega\textbackslashsubset\textbackslashmathbb R^n$ be a domain, let $K\textbackslashge 1$, and let $p\textbackslashge 1$. A mapping $f\textbackslashin W^{1,p}_{\textbackslashoperatorname{loc}}(cuOmega;\textbackslashmathbb R^n)$ is weakly $K$-quasiregular if it satisfies the corresponding weak distortion inequality. Iwaniec–Martin's conjecture. Every weakly $K$-quasiregular mapping $f\textbackslashin W^{1,p}_{\textbackslashoperatorname{loc}}(cuOmega;\textbackslashmathbb R^n)$ with $p\textbackslashge \frac{nK}{K+1}$ is $K$-quasiregular. The conjecture identifies the critical Sobolev exponent at which weak quasiregularity should imply quasiregularity; the cited discussion records examples below this threshold and the known optimality of the range when $n=2$, but does not state a resolution of the conjecture in general.