Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Khavinson-Shapiro conjecture for domains with a boundary consisting
  of algebraic hypersurfaces   The Khavinson-Shapiro conjecture states that ellipsoids are the only bounded
domains in euclidean space satisfying the following property (KS): the solution
of the Dirichlet problem for polynomial data is polynomial. In this paper we
show that a domain does not have property (KS) provided the boundary contains
at least three differrent irreducible algebraic hypersurfaces for which two of
them have a common point.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs