Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic
  operators via maximum principle   In this paper we study optimal lower and upper bounds for functionals
involving the first Dirichlet eigenvalue $\lambda_{F}(p,\Omega)$ of the
anisotropic $p$-Laplacian, $1<p<+\infty$. Our aim is to enhance how, by means
of the $\mathcal P$-function method, it is possible to get several sharp
estimates for $\lambda_{F}(p,\Omega)$ in terms of several geometric quantities
associated to the domain. The $\mathcal P$-function method is based on a
maximum principle for a suitable function involving the eigenfunction and its
gradient.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol