Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular boundary behaviour and large solutions for fractional elliptic
  equations   We show that the boundary behaviour of solutions to nonlocal fractional
equations posed in bounded domains strongly differs from the one of solutions
to elliptic problems modelled upon the Laplace-Poisson equation with zero
boundary data. In this classical case it is known that, at least in a suitable
weak sense, solutions of non-homogeneous Dirichlet problem are unique and tend
to zero at the boundary. Limits of these solutions then produce solutions of
some non-homogeneous Dirichlet problem as the interior data concentrate
suitably to the boundary. Here, we show that such results are false for
equations driven by a wide class of nonlocal fractional operators, extending
previous findings for some models of the fractional Laplacian operator.
Actually, different blow-up phenomena may occur at the boundary of the domain.
We describe such explosive behaviours and obtain precise quantitative estimates
depending on simple parameters of the nonlocal pperators. Our unifying
technique is based on a careful study of the inverse operator in terms of the
corresponding Green function.

28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph