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arXiv · 2301.11677

Strong unique continuation from the boundary for the spectral fractional Laplacian

Alessandra De Luca·Veronica Felli·Giovanni Siclari
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Abstract

We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian. An extension procedure leads us to study a degenerate or singular equation on a cylinder, with a homogeneous Dirichlet boundary condition on the lateral surface and a non homogeneous Neumann condition on the basis. For the extended problem, by an Almgren-type monotonicity formula and a blow-up analysis, we classify the local asymptotic profiles at the edge where the transition between boundary conditions occurs. Passing to traces, an analogous blow-up result and its consequent strong unique continuation property is deduced for the nonlocal fractional equation.

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Alessandra De Luca, Veronica Felli, Giovanni Siclari. 2023-01-27. Strong unique continuation from the boundary for the spectral fractional Laplacian. https://arxiv.org/abs/2301.11677

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