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arXiv · 1209.1998

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

Nam Q. Le·Truyen Nguyen
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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.

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Nam Q. Le, Truyen Nguyen. 2012-12-17. Global $W^{2,p}$ estimates for solutions to the linearized Monge--Ampère equations. https://doi.org/10.1007/s00205-013-0653-5

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