We show that as well as the classical isoperimetric inequalities, affine isoperimetric inequalities can be used to obtain a priori estimates for solutions to elliptic problems. In particular we show that the eigenvalue of the Dirichlet problem for the MongeAmpère operator, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result is established by exploiting the affine invariant structure of such operator using either Blaschke-Santalò or Petty inequalities.