Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasilinear elliptic and parabolic Robin problems on Lipschitz domains   We prove H\"older continuity up to the boundary for solutions of quasi-linear
degenerate elliptic problems in divergence form, not necessarily of variational
type, on Lipschitz domains with Neumann and Robin boundary conditions. This
includes the $p$-Laplace operator for all $p \in (1,\infty)$, but also
operators with unbounded coefficients. Based on the elliptic result we show
that the corresponding parabolic problem is well-posed in the space
$C(\bar{\Omega})$ provided that the coefficients satisfy a mild monotonicity
condition. More precisely, we show that the realization of the elliptic
operator in $C(\bar{\Omega})$ is m-accretive and densely defined. Thus it
generates a non-linear strongly continuous contraction semigroup on
$C(\bar{\Omega})$.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio