Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On principal frequencies and inradius in convex sets   We generalize to the case of the $p-$Laplacian an old result by Hersch and
Protter. Namely, we show that it is possible to estimate from below the first
eigenvalue of the Dirichlet $p-$Laplacian of a convex set in terms of its
inradius. We also prove a lower bound in terms of isoperimetric ratios and we
briefly discuss the more general case of Poincar\'e-Sobolev embedding
constants. Eventually, we highlight an open problem.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph