English

Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions

Analysis of PDEs 2017-08-30 v3

Abstract

We present some comparison results for solutions to certain non local elliptic and parabolic problems that involve the fractional Laplacian operator and mixed boundary conditions, given by a zero Dirichlet datum on part of the complementary of the domain and zero Neumann data on the rest. These results represent a non local generalization of a Hopf's lemma for elliptic and parabolic problems with mixed conditions. In particular we prove the non local version of the results obtained by J. D\'avila and J. D\'avila-L. Dupaigne for the classical case respectively.

Keywords

Cite

@article{arxiv.1607.01505,
  title  = {Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions},
  author = {Begoña Barrios and María Medina},
  journal= {arXiv preprint arXiv:1607.01505},
  year   = {2017}
}