Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of spectral fractional Dirichlet and Neumann problems   Consider the fractional powers $(A_{\operatorname{Dir}})^a$ and
$(A_{\operatorname{Neu}})^a$ of the Dirichlet and Neumann realizations of a
second-order strongly elliptic differential operator $A$ on a smooth bounded
subset $\Omega $ of ${\Bbb R}^n$. Recalling the results on complex powers and
complex interpolation of domains of elliptic boundary value problems by Seeley
in the 1970's, we demonstrate how they imply regularity properties in full
scales of $H^s_p$-Sobolev spaces and H\"older spaces, for the solutions of the
associated equations. Extensions to nonsmooth situations for low values of $s$
are derived by use of recent results on $H^\infty $-calculus. We also include
an overview of the various Dirichlet- and Neumann-type boundary problems
associated with the fractional Laplacian.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph