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Global \(W^{2,p}\) estimates for solutions to the linearized Monge–Ampère equations

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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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Acknowledgments

T. Nguyen gratefully acknowledges the support provided by NSF grant DMS-0901449.

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Correspondence to Truyen Nguyen.

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Le, N.Q., Nguyen, T. Global \(W^{2,p}\) estimates for solutions to the linearized Monge–Ampère equations. Math. Ann. 358, 629–700 (2014). https://doi.org/10.1007/s00208-013-0974-6

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  • DOI: https://doi.org/10.1007/s00208-013-0974-6

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