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arXiv · 1602.02194

Global $W^{1,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations

Nam Q. Le·Truyen Nguyen
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Abstract

In this paper, we investigate regularity for solutions to the linearized Monge-Amp\`ere equations when the nonhomogeneous term has low integrability. We establish global $W^{1,p}$ estimates for all $p<\frac{nq}{n-q}$ for solutions to the equations with right hand side in $L^q$ where $n/2<q\leq n$. These estimates hold under natural assumptions on the domain, Monge-Amp\`ere 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.

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Nam Q. Le, Truyen Nguyen. 2016-02-06. Global $W^{1,p}$ estimates for solutions to the linearized Monge--Amp\`ere equations. https://arxiv.org/abs/1602.02194

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