Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal Sobolev regularity for solutions of elliptic equations in
  infinite dimensional Banach spaces endowed with a weighted Gaussian measure   Let $X$ be a separable Banach space endowed with a non-degenerate centered
Gaussian measure $\mu$. The associated Cameron-Martin space is denoted by $H$.
Let $\nu=e^{-U}\mu$, where $e^{-U}$ is a sufficiently regular weight and
$U:X\rightarrow\mathbb{R}$ is a convex and continuous function. In this paper
we are interested in the $W^{2,2}$ regularity of the weak solutions of elliptic
equations of the type \[\lambda u-L_\nu u=f,\] where $\lambda>0$, $f\in
L^2(X,\nu)$ and $L_\nu$ is the self-adjoint operator associated with the
quadratic form \[(\psi,\varphi)\mapsto
\int_X\left\langle\nabla_H\psi,\nabla_H\varphi\right\rangle_Hd\nu\qquad\psi,\varphi\in
W^{1,2}(X,\nu).\]

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph