Continuity under the critical Lebesgue-space assumption

Determine whether every solution u in W^{1,n/(n-1)}(B^n, R^m) of the critical elliptic system -Δu = Ω · ∇u in the distributional sense, with antisymmetric potential Ω in L^n(B^n, so(m) ⊗ Λ^1), necessarily belongs to C^0(B^n).

Background

The paper proves continuity for solutions of -Δu = Ω * ∇u in dimensions n ≥ 3 when Ω belongs to the finer Lorentz space L^{(n,q)} with 1 ≤ q ≤ 2, under the smallness condition required by the gauge construction, and when u belongs to W^{1,(n/(n-1),q')}. The question asks whether the endpoint Lebesgue-space assumption Ω ∈ L^n is sufficient without the stronger Lorentz-space hypothesis.

This is explicitly presented as an unresolved problem under milder assumptions. It concerns whether the regularity mechanism established in the paper extends to the critical system with the weaker integrability Ω ∈ L^n and the corresponding endpoint solution space W^{1,n/(n-1)}.