Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Null quadrature domains and a free boundary problem for the Laplacian   Null quadrature domains are unbounded domains in $\R^n$ ($n \geq 2$) with
external gravitational force zero in some generalized sense. In this paper we
prove that the complement of null quadrature domain is a convex set with real
analytic boundary. We establish the quadratic growth estimate for the Schwarz
potential of a null quadrature domain which reduces our main result to Theorem
II of the paper of Caffarelli, Karp and Shahgholian (Ann. Math. 151(2000),
269-292), on the regularity of solution to the classical global free boundary
problem for Laplacian. We also show that any null quadrature domain with
non-zero upper Lebesgue density at infinity is half-space.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom