Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Description of All Self-Adjoint Extensions of the Laplacian and
  Krein-Type Resolvent Formulas on Nonsmooth Domains   This paper has two main goals. First, we are concerned with the
classification of self-adjoint extensions of the Laplacian
$-\Delta\big|_{C^\infty_0(\Omega)}$ in $L^2(\Omega; d^n x)$. Here, the domain
$\Omega$ belongs to a subclass of bounded Lipschitz domains (which we term
quasi-convex domains), which contain all convex domains, as well as all domains
of class $C^{1,r}$, for $r\in(1/2,1)$. Second, we establish Krein-type formulas
for the resolvents of the various self-adjoint extensions of the Laplacian in
quasi-convex domains and study the properties of the corresponding
Weyl--Titchmarsh operators (or energy-dependent Dirichlet-to-Neumann maps).
  One significant technical innovation in this paper is an extension of the
classical boundary trace theory for functions in spaces which lack Sobolev
regularity in a traditional sense, but are suitably adapted to the Laplacian.

10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom