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arXiv · 1607.01505

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

Begoña Barrios·María Medina
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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.

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Begoña Barrios, María Medina. 2016-07-06. Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions. https://arxiv.org/abs/1607.01505

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