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. D\'avila 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.
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Analysis of PDEs
35B50, 35R11, 35S15
