Gradient regularity for quasilinear elliptic Dirichlet problems in the plane

The problem is addressed of the maximal integrability of the gradient of solutions to quasilinear elliptic equations, with merely measurable coefficients, in two variables. Optimal results are obtained in the framework of Orlicz spaces, and in the more general setting of all rearrangement-invariant spaces. Applications to special instances are exhibited. In particular, various results available in the literature are recovered, or even improved.