Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary regularity of the solution to the Complex Monge-Amp\`{e}re
  equation on pseudoconvex domains of infinite type   Let $\Omega$ be a bounded, pseudoconvex domain of $\mathbb C^n$ satisfying
the "$f$-Property". The $f$-Property is a consequence of the geometric "type"
of the boundary; it holds for all pseudoconvex domains of finite type but may
also occur for many relevant classes of domains of infinite type. In this
paper, we prove the existence, uniqueness and "weak" H\"older-regularity up to
the boundary of the solution to the Dirichlet problem for the complex
Monge-Amp\`{e}re equation $$ \begin{cases}
\det\left[\dfrac{\partial^2(u)}{\partial z_i\partial\bar z_j}\right]=h\ge 0 &
\text{in}\quad\Omega,\\ u=\phi & \text{on} \quad b\Omega. \end{cases} $$

7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int