Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak and renormalized solutions to a hypoelliptic Mean Field Games
  system   We establish the existence and uniqueness of weak and renormalized solutions
to a degenerate, hypoelliptic Mean Field Games system with local coupling. An
important step is to obtain $L^{\infty}-$bounds for solutions to a degenerate
Fokker-Planck equation with a De-Giorgi type argument. In particular, we show
existence and uniqueness of weak solutions to Mean Fields Games systems with
Lipschitz Hamiltonians. Furthermore, we establish existence and uniqueness of
renormalized solutions for Hamiltonians with quadratic growth. Our approach
relies on the kinetic regularity of hypoelliptic equations obtained by Bouchut
and the work of Porretta on the existence and uniqueness of renormalized
solutions for the Mean Field Game system, in the non-degenerate setting.

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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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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: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph