Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kiselman's principle, the Dirichlet problem for the Monge-Ampere
  equation, and rooftop obstacle problems   First, we obtain a new formula for Bremermann type upper envelopes, that
arise frequently in convex analysis and pluripotential theory, in terms of the
Legendre transform of the convex- or plurisubharmonic-envelope of the boundary
data. This yields a new relation between solutions of the Dirichlet problem for
the homogeneous real and complex Monge-Ampere equations and Kiselman's minimum
principle. More generally, it establishes partial regularity for a Bremermann
envelope whether or not it solves the Monge-Ampere equation. Second, we prove
the second order regularity of the solution of the free-boundary problem for
the Laplace equation with a rooftop obstacle, based on a new a priori estimate
on the size of balls that lie above the non-contact set. As an application, we
prove that convex- and plurisubharmonic-envelopes of rooftop obstacles have
bounded second derivatives.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg