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

Abstract

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.

13 pages, This paper is published in Fract. Calc. Appl. Anal., Vol. 24, No 6 (2021), pp. 1699 1715, so cite it with the journal coordinates