Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence of solutions of eikonal equation in metric spaces   In this paper we prove the equivalence between some known notions of
solutions to the eikonal equation and more general analogs of the
Hamilton-Jacobi equations in complete and rectifiably connected metric spaces.
The notions considered are that of curve-based viscosity solutions, slope-based
viscosity solutions, and Monge solutions. By using the induced intrinsic (path)
metric, we reduce the metric space to a length space and show the equivalence
of these solutions to the associated Dirichlet boundary problem. Without
utilizing the boundary data, we also localize our argument and directly prove
the equivalence for the definitions of solutions. Regularity of solutions
related to the Euclidean semi-concavity is discussed as well.

5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys