Global $W^{1,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations
Analysis of PDEs
2016-02-09 v1
Abstract
In this paper, we investigate regularity for solutions to the linearized Monge-Amp\`ere equations when the nonhomogeneous term has low integrability. We establish global estimates for all for solutions to the equations with right hand side in where . These estimates hold under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant analogues of the global estimates of N. Winter for fully nonlinear, uniformly elliptic equations.
Keywords
Cite
@article{arxiv.1602.02194,
title = {Global $W^{1,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations},
author = {Nam Q. Le and Truyen Nguyen},
journal= {arXiv preprint arXiv:1602.02194},
year = {2016}
}