A Strong Maximum Principle for the fractional Laplace equation with mixed boundary condition

In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. Dávila to the fractional setting. In particular, we present a comparison result for two solutions of the fractional Laplace equation involvi...

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Bibliographic Details
Published in:arXiv.org 2021-11
Main Authors: López-Soriano, Rafael, Ortega, Alejandro
Format: Article
Language:English
Subjects:
Boundary conditions
Dirichlet problem
Laplace equation
Maximum principle
Online Access:Get full text
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Summary:In this work we prove a strong maximum principle for fractional elliptic problems with mixed Dirichlet-Neumann boundary data which extends the one proved by J. Dávila to the fractional setting. In particular, we present a comparison result for two solutions of the fractional Laplace equation involving the spectral fractional Laplacian endowed with homogeneous mixed boundary condition. This result represents a non-local counterpart to a Hopf's Lemma for fractional elliptic problems with mixed boundary data.
ISSN:2331-8422
DOI:10.48550/arxiv.2103.04735