Theorem 1.3 . [04TM]

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Theorem 1.3.

Assume that

\det D^{2}u=\det D^{2}v=f

in an open connected set $\Omega\subset\mathbb{R}^{n}$ , with $f\in C^{1,\alpha}(\Omega)$ strictly positive. If $u=v$ on an open subset of $\Omega$ , then $u\equiv v$ in $\Omega$ .