Boundary Harnack inequality for the linearized Monge-Ampère equations and applications

Le, Nam

doi:10.1090/tran/7220

Boundary Harnack inequality for the linearized Monge-Ampère equations and applications
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by Nam Q. Le PDF

Trans. Amer. Math. Soc. 369 (2017), 6583-6611 Request permission

Abstract:

In this paper, we obtain boundary Harnack estimates and comparison theorem for nonnegative solutions to the linearized Monge-Ampère equations under natural assumptions on the domain, Monge-Ampère measures and boundary data. Our results are boundary versions of Caffarelli and Gutiérrez’s interior Harnack inequality for the linearized Monge-Ampère equations. As an application, we obtain sharp upper bound and global $L^p$-integrability for Green’s function of the linearized Monge-Ampère operator.

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