Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularizing effect of homogeneous evolution equations: case homogeneous
  order zero   In this paper, we develop a functional analytical theory for establishing
that mild solutions of first-order Cauchy problems involving homogeneous
operators of order zero are strong solutions; in particular, the first-order
time derivative satisfies a global regularity estimate depending only on the
initial value and the positive time. We apply those results to the Cauchy
problem associated with the total variational flow operator and the nonlocal
fractional 1-Laplace operator.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat