Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The vanishing discount problem and viscosity Mather measures. Part 1:
  the problem on a torus   We develop a variational approach to the vanishing discount problem for fully
nonlinear, degenerate elliptic, partial differential equations. Under mild
assumptions, we introduce viscosity Mather measures for such partial
differential equations, which are natural extensions of the Mather measures.
Using the viscosity Mather measures, we prove that the whole family of
solutions $v^\lambda$ of the discount problem with the factor $\lambda>0$
converges to a solution of the ergodic problem as $\lambda \to 0$.

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The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn