Global W2,p estimates for solutions to the linearized Monge–Ampère equations

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, un...

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Bibliographic Details
Published in:Mathematische annalen 2014, Vol.358 (3-4), p.629-700
Main Authors: Le, Nam Q., Nguyen, Truyen
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-013-0974-6