On the free boundary associated to the stationary Monge–Ampère operator on the set of non strictly convex functions

Díaz Díaz, GregorioDíaz Díaz, Jesús Ildefonso2023-06-182023-06-182015-041078-094710.3934/dcds.2015.35.1447https://hdl.handle.net/20.500.14352/22978This paper deals with several qualitative properties of solutions of some stationary equations associated to the Monge-Ampere 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.engOn the free boundary associated to the stationary Monge–Ampère operator on the set of non strictly convex functionsjournal articlehttps://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10562https://www.aimsciences.org/index.htmlopen access517.9Monge-Ampere equationGauss curvature surfacesfree boundary problemEcuaciones diferenciales1202.07 Ecuaciones en Diferencias