Global \(W^{1,p}\) estimates for solutions to the linearized Monge-Ampère equations (Q2411185)

The authors investigate the regularity of the solutions to the linearized Monge-Ampére equation when the nonhomogenous term has low integrability. The main result establishes global \(W^{1,p}\) estimates, \(p<\frac{nq}{n-q}\), if the right hand side belongs to \(L^q\), \(n/2<q\leq n\). These estimates hold under natural assumptions on the domain, the Monge-Ampére measures, and boundary data. There are also a proof for an interior maximun priciple, an interior Hölder estimate, and a proof of global \(W^{1,p}\) and Hölder estimates.