The obstacle problem for a fractional Monge–Ampère equation

Abstract

We study the obstacle problem for a nonlocal, degenerate elliptic Monge-Ampère equation. We show existence and regularity of a unique classical solution to the problem and regularity of the free boundary. A∈M tr(A 2 D 2 u)(x). If, in addition, u is asymptotically linear at infinity, then lim s→1 D s u(x) = n(det D 2 u(x)) 1/n 2010 Mathematics Subject Classification. Primary: 35J96, 35R35, 35R11. Secondary: 35B65, 35J60, 47G20.