Calabi-Bernstein type theorems for entire solutions of certain nonlinear elliptic equations in the plane

Abstract

We provide some extensions of the classical Calabi-Bernstein theorem to the case of entire solutions of certain nonlinear elliptic equations in two variables. Using an appropriate version of the Calabi correspondence, which formulates a duality between minimal graphs in ${\mathbb{R}}^3$ and maximal spacelike graphs in ${\mathbb{L}}^3$, our results are a consequence of recent Bernstein type results.