On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two

Jean Dolbeault & Régis Monneau
In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in IR2. We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.
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