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Corpus ID: 203610465

Singular boundary behaviour and large solutions for fractional elliptic equations.

@article{Abatangelo2019SingularBB,
title={Singular boundary behaviour and large solutions for fractional elliptic equations.},
author={Nicola Abatangelo and D. G{\'o}mez-Castro and J. V{\'a}zquez},
journal={arXiv: Analysis of PDEs},
year={2019}
}

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… CONTINUE READING