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 (cf. [11]) 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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López-Soriano, R., Ortega, A. A Strong Maximum Principle for the Fractional Laplace Equation with Mixed Boundary Condition. Fract Calc Appl Anal 24, 1699–1715 (2021). https://doi.org/10.1515/fca-2021-0073
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DOI: https://doi.org/10.1515/fca-2021-0073