Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness of renormalized solutions for a stochastic $p$-Laplace
  equation with $L^1$-initial data   We consider a $p$-Laplace evolution problem with stochastic forcing on a
bounded domain $D\subset\mathbb{R}^d$ with homogeneous Dirichlet boundary
conditions for $1<p<\infty$. The additive noise term is given by a stochastic
integral in the sense of It\^{o}. The technical difficulties arise from the
merely integrable random initial data $u_0$ under consideration. Due to the
poor regularity of the initial data, estimates in $W^{1,p}_0(D)$ are available
with respect to truncations of the solution only and therefore well-posedness
results have to be formulated in the sense of generalized solutions. We extend
the notion of renormalized solution for this type of SPDEs, show well-posedness
in this setting and study the Markov properties of solutions.

27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics