Green function representation and summability properties for elliptic equations in double divergence form with Morrey data

In this paper adjoint solutions to second–order elliptic equations in double divergence form with low–integrability data are investigated. We show that adjoint solutions with right–hand side in L1(Ω) admit a Green function representation under mild regularity on the leading coefficients, yielding existence and uniqueness in L1(Ω). When the datum belongs to a Morrey space L1,λ(Ω), we exploit refined estimates for the Green kernel to derive improved integrability and boundedness properties of the corresponding adjoint solution. The results highlight the natural role of Green function methods in the analysis of adjoint problems with rough data.