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arXiv · 2103.04665

Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations

Alessandra De Luca·Veronica Felli·Stefano Vita
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Abstract

We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulae and provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.

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Alessandra De Luca, Veronica Felli, Stefano Vita. 2021-03-08. Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations. https://doi.org/10.1016/j.aim.2022.108279

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