Generalized structural conditions for a Calderón-Zygmund theory on double phase problems

In this paper, we considered a general class of double-phase problems of the form$ - {{\rm{div}}} (A(x, Du)) = - {{\rm{div}}}( B(x, F)). $Here, the ellipticity, growth, and continuity assumptions on the main operator $ A $ were described using an auxiliary vector field $ G $. The proposed structural condition allowed us to treat, in a single setting, different structural forms that have appeared in earlier studies. Under this generalized structure, we derived Calderón-Zygmund estimates for the gradients of solutions.