The non-radial extension conjecture for planar mappings of finite distortion

Let $f$ be a planar homeomorphic mapping of finite distortion satisfying the hypotheses of Theorem $\mathrm{}$, except that radiality is not assumed. The conclusions of Theorem $\mathrm{}$ remain true without assuming that the map is radial. This conjecture asserts that the improved local integrability conclusions established for radial mappings extend to all planar homeomorphic mappings under the same distortion assumptions.