Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the Green's function of the linearized Monge-Amp\`ere
  operator   In this note, we obtain sharp bounds for the Green's function of the
linearized Monge-Amp\`ere operators associated to convex functions with either
Hessian determinant bounded away from zero and infinity or Monge-Amp\`ere
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 $L^{p}$ 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-Amp\`ere
equation.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga