Symmetry of global solutions to a class of fully nonlinear elliptic equations in 2D D. De SilvaO. Savin 35J60phase transitionviscosity solutionsDe Giorgi conjecture We prove that entire bounded monotone solutions to fully nonlinear equations in $\mathbb{R}^2$ of the form $F(D^2u) = f(u)$ are one-dimensional, under appropriate compatibility conditions for $F$ and $f$. In the particular case when $F = \Delta$ and $f(u) = u^3-u$, our result gives a new (non-variational) proof of the well known De Giorgi's conjecture. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3396 10.1512/iumj.2009.58.3396 en Indiana Univ. Math. J. 58 (2009) 301 - 316 state-of-the-art mathematics http://iumj.org/access/