Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the vanishing viscosity process of state-constraint
  Hamilton-Jacobi equations   We investigate the convergence rate in the vanishing viscosity process of the
solutions to the subquadratic state-constraint Hamilton-Jacobi equations. We
give two different proofs of the fact that, for nonnegative Lipschitz data that
vanish on the boundary, the rate of convergence is
$\mathcal{O}(\sqrt{\varepsilon})$ in the interior. Moreover, the one-sided rate
can be improved to $\mathcal{O}(\varepsilon)$ for nonnegative compactly
supported data and $\mathcal{O}(\varepsilon^{1/p})$ (where $1<p<2$ is the
exponent of the gradient term) for nonnegative data $f\in
\mathrm{C}^2(\bar{\Omega})$ such that $f = 0$ and $Df = 0$ on the boundary. Our
approach relies on deep understanding of the blow-up behavior near the boundary
and semiconcavity of the solutions.

25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph