Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak solutions for first order mean field games with local coupling   Existence and uniqueness of a weak solution for first order mean field game
systems with local coupling are obtained by variational methods. This solution
can be used to devise $\epsilon-$Nash equilibria for deterministic differential
games with a finite (but large) number of players. For smooth data, the first
component of the weak solution of the MFG system is proved to satisfy (in a
viscosity sense) a time-space degenerate elliptic differential equation.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: cs