Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On viscosity and equivalent notions of solutions for anisotropic
  geometric equations   We prove that viscosity solutions of geometric equations in step two Carnot
groups can be equivalently reformulated by restricting the set of test
functions at the singular points. These are characteristic points for the level
sets of the solutions and are usually difficult to deal with. A similar
property is known in the euclidian space, and in Carnot groups is based on
appropriate properties of a suitable homogeneous norm. We also use this idea to
extend to Carnot groups the definition of generalised flow, and it works
similarly to the euclidian setting. These results simplify the handling of the
singularities of the equation, for instance to study the asymptotic behaviour
of singular limits of reaction diffusion equations. We provide examples of
using the simplified definition, showing for instance that boundaries of
strictly convex subsets in the Carnot group structure become extinct in finite
time when subject to the horizontal mean curvature flow even if characteristic
points are present.

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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn