Universidad Complutense de Madrid
E-Prints Complutense

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

Impacto

Downloads

Downloads per month over past year

Díaz Díaz, Gregorio and Díaz Díaz, Jesús Ildefonso (2015) On the free boundary associated to the stationary Monge–Ampère operator on the set of non strictly convex functions. Discrete and Continuous Dynamical Systems. Series A., 35 (4). pp. 1447-1468. ISSN 1078-0947

[img]
Preview
PDF
308kB

Official URL: https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10562




Abstract

This 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.


Item Type:Article
Uncontrolled Keywords:Monge-Ampere equation; Gauss curvature surfaces; free boundary problem
Subjects:Sciences > Mathematics > Differential equations
ID Code:28350
Deposited On:12 Feb 2015 13:40
Last Modified:12 Dec 2018 15:06

Origin of downloads

Repository Staff Only: item control page