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}
}

Nicola Abatangelo, D. Gómez-Castro, J. Vázquez

Published 2019

Mathematics

arXiv: Analysis of PDEs

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

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