Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the global regularity for minimizers of variational integrals:
  splitting-type problems in 2D and extensions to the general anisotropic
  setting   We mainly discuss superquadratic minimization problems for splitting-type
variational integrals on a bounded Lipschitz domain $\Omega \subset
\mathbb{R}^2$ and prove higher integrability of the gradient up to the boundary
by incorporating an appropriate weight-function measuring the distance of the
solution to the boundary data. As a corollary, the local H\"older coefficient
with respect to some improved H\"older continuity is quantified in terms of the
function ${\rm dist}(\cdot,\partial \Omega)$. The results are extended to
anisotropic problems without splitting structure under natural growth and
ellipticity conditions. In both cases we argue with variants of Caccioppoli's
inequality involving small weights

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int