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We study the equation $u_{11}u_{22} = 1$ in $\mathbb{R}^2$. Our resultsinclude an interior $C^2$ estimate, classical solvability of the Dirichletproblem, and the existence of non-quadratic entire solutions. We also constructglobal singular solutions to the analogous equation in higher dimensions. Atthe end we state some open questions.

Regularity results for the equation $u_{11}u_{22} = 1$