Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalue Problems in $\mathrm{L}^\infty$: Optimality Conditions,
  Duality, and Relations with Optimal Transport   In this article we characterize the $\mathrm{L}^\infty$ eigenvalue problem
associated to the Rayleigh quotient $\left.{\|\nabla
u\|_{\mathrm{L}^\infty}}\middle/{\|u\|_\infty}\right.$, defined on Lipschitz
functions with homogeneous boundary conditions on a domain $\Omega$. For this,
we derive a novel fine characterization of the subdifferential of the
functional $u\mapsto\|\nabla u\|_{\mathrm{L}^\infty}$. Using the concept of
tangential gradients we show that it consists of Radon measures of the form
$-\operatorname{div}\sigma$ where $\sigma$ is a normalized divergence-measure
field, in a suitable sense parallel to the gradient $\nabla u$ and concentrated
where it is maximal. We also investigate geometric relations between general
minimizers of the Rayleigh quotient and suitable distance functions. Lastly, we
investigate a "dual" Rayleigh quotient whose minimizers are subgradients of
minimizers of the original quotient and solve an optimal transport problem
associated to a generalized Kantorovich-Rubinstein norm. Our results apply to
all minimizers of the Rayleigh quotient, including infinity ground states,
infinity harmonic potentials, distance functions, etc., and generalize known
results in the literature.

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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
9
The categories of this paper are: nlin
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: cs