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PROC

This paper deals with several qualitative properties of solutions of some parabolic equations associated to the Monge--Ampère operator arising in suitable formulations of the Gauss curvature flow and the worn stone problems.

DCDS

This paper deals with several qualitative properties of solutions of some stationary equations associated to the Monge--Ampère
operator on the set of convex functions which are not necessarily understood in a strict sense. Mainly, we focus our attention on the
occurrence of a free boundary (separating the region where the solution $u$ is locally a hyperplane, thus, the Hessian $D^{2}u$
is vanishing, from the rest of the domain). In particular, our results apply to suitable formulations of the Gauss curvature flow and of the worn stones problems intensively studied in the literature.

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