Existence, uniqueness, regularity and stability of solutions to linear X-elliptic equations with measurable coefficients

We prove an existence and uniqueness result for solutions to linear X-elliptic equations with L¹ data and zero Dirichlet boundary conditions. Such solutions depend continuously on the datum. Moreover, we show that an improvement in the summability of the data yields a corresponding improvement in the summability of the solutions, in a manner analogous to the one that occurs in the case of uniformly elliptic equations.