Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On regularity properties of solutions to the hysteresis-type problems   We consider equations with the simplest hysteresis operator at the right-hand
side. Such equations describe the so-called processes "with memory" in which
various substances interact according to the hysteresis law.
  We restrict our consideration on the so-called "strong solutions" belonging
to the Sobolev class $W^{2,1}_q$ with sufficiently large $q$ and prove that in
fact $q=\infty$. In other words, we establish the optimal regularity of
solutions. Our arguments are based on quadratic growth estimates for solutions
near the free boundary.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas