Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A nonlocal biharmonic operator and its connection with the classical
  analogue   We introduce here a nonlocal operator as a natural generalization to the
biharmonic operator that appears in plate theory. This operator is built in the
nonlocal calculus framework defined by Du et al. and its connected with the
recent theory of peridynamics. For the steady state equation coupled with
different boundary conditions we show existence and uniqueness of solutions, as
well as regularity of solutions. The boundary conditions considered are
nonlocal counterparts of the classical clamped and hinged boundary conditions.
For each system we show convergence of the nonlocal solutions to their local
equivalents using compactness arguments developed by Bourgain, Brezis and
Mironescu.

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The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph