Gradient estimates for nonlinear elliptic equations 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, which provide new gradient bounds, or improve certain
results available in the literature.