Global $W^{2,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations

Nam Q. Le; Truyen Nguyen

doi:10.1007/s00205-013-0653-5

Global $W^{2,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations

Analysis of PDEs 2015-06-11 v2

Authors: 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-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere 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-Amp\`ere equations.

Keywords

complex monge-ampère equation gradient estimates

Cite

@article{arxiv.1209.1998,
  title  = {Global $W^{2,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations},
  author = {Nam Q. Le and Truyen Nguyen},
  journal= {arXiv preprint arXiv:1209.1998},
  year   = {2015}
}

Comments

v2: presentation improved

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