Remarks on the Green’s function of the linearized Monge–Ampère operator
Remarks on the Green’s function of the linearized Monge–Ampère operator
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关于线性化 Monge-Ampère 算子的 Green 函数的评论
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
N. Le
中科院分区：
文献类型：
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作者：
N. Le
本文得到了与Hessian行列式远离零和无穷有界的凸函数或Monge-Ampère测度满足加倍条件的凸函数相关联的线性化Monge-Ampère算子的绿色函数的精确界.我们的结果是Littman-Stampacchia-Weinberger关于散度型一致椭圆算子的经典结果的仿射不变版本。我们还得到了二维绿色函数梯度的Lp可积性。作为应用，我们得到了线性化的Monge-Ampère方程的一个可去奇异性结果.
In this note, we obtain sharp bounds for the Green’s function of the linearized Monge–Ampère operators associated to convex functions with either Hessian determinant bounded away from zero and infinity or Monge–Ampère measure satisfying a doubling condition. Our result is an affine invariant version of the classical result of Littman–Stampacchia–Weinberger for uniformly elliptic operators in divergence form. We also obtain the Lp integrability for the gradient of the Green’s function in two dimensions. As an application, we obtain a removable singularity result for the linearized Monge–Ampère equation.