Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit estimates for solutions of nonlinear radiation-type problems   We establish the existence of weak solutions of a nonlinear radiation-type
boundary value problem for elliptic equation on divergence form with
discontinuous leading coefficient. Quantitative estimates play a crucial role
on the real applications. Our objective is the derivation of explicit
expressions of the involved constants in the quantitative estimates, the
so-called absolute or universal bounds. The dependence on the leading
coefficient and on the size of the spatial domain is precise.This work shows
that the expressions of those constants are not so elegant as we might expect.

3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex