We prove that entire bounded monotone solutions to a certain class of fully nonlinear equations in 2D are one-dimensional. Our result also gives a new (non-variational) proof of the well known De Giorgi's conjecture.
Nonclassical Solutions of Fully Nonlinear Elliptic Equations
On the existence of $W^{2}_{p}$ solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions
On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions
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