Global W 1 , p estimates for solutions to the linearized Monge–Ampère equations

In this paper, we investigate regularity for solutions to the linearized Monge–Ampère equations when the nonhomogeneous term has low integrability. We establish global W 1 , p estimates for all p < n q n - q for solutions to the equations with right-hand side in L q where n / 2 < q ≤ n . These...

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Bibliographic Details
Published in:The Journal of geometric analysis 2017-01, Vol.27 (3), p.1751-1788
Main Authors: Le, Nam Q, Nguyen, Truyen
Format: Article
Language:English
Subjects:
Estimates
Geometry
Mathematical analysis
Regularity
Online Access:Get full text
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Summary:In this paper, we investigate regularity for solutions to the linearized Monge–Ampère equations when the nonhomogeneous term has low integrability. We establish global W 1 , p estimates for all p < n q n - q for solutions to the equations with right-hand side in L q where n / 2 < q ≤ n . These estimates hold under natural assumptions on the domain, Monge–Ampère measures, and boundary data. Our estimates are affine invariant analogues of the global W 1 , p estimates of N. Winter for fully nonlinear, uniformly elliptic equations.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-016-9739-2