Global $W^{2,p}$ estimates for solutions to the linearized Monge--Ampère equations

Abstract

In this paper, we establish global $W^{2,p}$ estimates for solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our estimates are affine invariant analogues of the global $W^{2,p}$ estimates of Winter for fully nonlinear, uniformly elliptic equations, and also linearized counterparts of Savin's global $W^{2,p}$ estimates for the Monge-Ampère equations.

v2: presentation improved

Cited by in corpus (1)

• Twisted Harnack inequality and approximation of variational problems with a convexity constraint by singular Abreu equations