Communications in Analysis and Geometry

Volume 24 (2016)

Number 2

A non-local Monge–Ampère equation

Pages: 307 – 335



Luis Caffarelli (Department of Mathematics, University of Texas, Austin, Tx., U.S.A.)

Luis Silvestre (Department of Mathematics, University of Chicago, Illinois, U.S.A.)


We introduce a non-local analog to the Monge–Ampère operator and show some of its properties. We prove that a global problem involving this operator has $C^{1,1}$ solutions in the full space.

Published 14 June 2016