Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher differentiability results in the scale of Besov spaces to a class
  of double-phase obstacle problems   We study the higher fractional differentiability properties of the gradient
of the solutions to variational obstacle problems of the form \begin{gather*}
\min \biggl\{ \int_{\Omega} F(x,w,Dw) d x \ : \ w \in
\mathcal{K}_{\psi}(\Omega) \biggr\}, \end{gather*} with $F$ double phase
functional of the form \begin{equation*} F(x,w,z)=b(x,w)(|z|^p+a(x)|z|^q),
\end{equation*} where $\Omega$ is a bounded open subset of $\mathbb{R}^n$,
$\psi \in W^{1,p}(\Omega)$ is a fixed function called \textit{obstacle} and
$\mathcal{K}_{\psi}(\Omega)= \{ w \in W^{1,p}(\Omega) : w \geq \psi \
\text{a.e. in} \ \Omega \}$ is the class of admissible functions. Assuming that
the gradient of the obstacle belongs to a suitable Besov space, we are able to
prove that the gradient of the solution preserves some fractional
differentiability property.

29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol