Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local strict singular characteristics II: existence for stationary
  equation on $\mathbb{R}^2$   The notion of strict singular characteristics is important in the
wellposedness issue of singular dynamics on the cut locus of the viscosity
solutions. We provide an intuitive and rigorous proof of the existence of the
strict singular characteristics of Hamilton-Jacobi equation $H(x,Du(x),u(x))=0$
in two dimensional case. We also proved if $\mathbf{x}$ is a strict singular
characteristic, then we really have the right-differentiability of $\mathbf{x}$
and the right-continuity of $\dot{\mathbf{x}}^+(t)$ for every $t$. Such a
strict singular characteristic must give a selection $p(t)\in
D^+u(\mathbf{x}(t))$ such that $p(t)=\arg\min_{p\in
D^+u(\mathbf{x}(t))}H(\mathbf{x}(t),p,u(\mathbf{x}(t)))$.

36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn