Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic solutions for the approximation of $p$-Laplacian problem   This paper mainly investigates the analytic solutions for the approximation
of $p$-Laplacian problem. Through an approximation mechanism, we convert the
nonlinear partial differential equation with Dirichlet boundary into a sequence
of minimization problems. And a sequence of analytic minimizers can be obtained
by applying the canonical duality theory. Moreover, the nonlinear canonical
transformation gives a sequence of perfect dual maximization(minimization)
problems, and further discussion shows the global extrema for both primal and
dual problems.

34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex