Local vanishing conjecture for rational singularities

Let $Z$ be a complex variety of dimension $n\geq 2$ with rational singularities, and let $f\colon Y\to Z$ be a resolution of singularities whose reduced exceptional divisor $E$ has simple normal crossings. Local vanishing conjecture. One has

$$R^{n-1}f_*\Omega_Y(\log E)=0.$$

This conjecture is proved when $Z$ has isolated singularities and when $Z$ is a toric variety; the general case remains open.