Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rearrangement inequalities and applications to isoperimetric problems
  for eigenvalues   Let $\Omega$ be a bounded $C^{2}$ domain in $\R^n$, and let $\Omega^{\ast}$
be the Euclidean ball centered at 0 and having the same Lebesgue measure as
$\Omega$. Consider the operator $L=-\div(A\nabla)+v\cdot \nabla +V$ on $\Omega$
with Dirichlet boundary condition. We prove that minimizing the principal
eigenvalue of $L$ when the Lebesgue measure of $\Omega$ is fixed and when $A$,
$v$ and $V$ vary under some constraints is the same as minimizing the principal
eigenvalue of some operators $L^*$ in the ball $\Omega^*$ with smooth and
radially symmetric coefficients. The constraints which are satisfied by the
original coefficients in $\Omega$ and the new ones in $\Omega^*$ are expressed
in terms of some distribution functions or some integral, pointwise or
geometric quantities. Some strict comparisons are also established when
$\Omega$ is not a ball.

5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph