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arXiv · 2405.12718

Unique continuation from conical boundary points for fractional equations

Alessandra De Luca·Veronica Felli·Stefano Vita
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Abstract

We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an approximation scheme, which allow us to provide a Pohozaev type inequality. Then, the asymptotics of solutions at the conical point follow by an Almgren type monotonicity formula, blow-up analysis and Fourier decomposition on eigenspaces of a spherical eigenvalue problem. A strong unique continuation principle follows as a corollary.

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Alessandra De Luca, Veronica Felli, Stefano Vita. 2024-05-21. Unique continuation from conical boundary points for fractional equations. https://doi.org/10.1137/24m1663193

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