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arXiv · 2607.29547

Edge asymptotics for weighted Robin equations on cylinders with applications to spectral fractional Laplacians

Alessandra De Luca·Veronica Felli·Stefano Vita
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Abstract

For a class of weighted degenerate or singular problems on a cylinder, Almgren-type monotonicity methods are employed to derive asymptotic estimates of solutions near the edge between the base and the lateral surface, where a Robin boundary condition is imposed. As a relevant application, local asymptotics and unique continuation from the boundary are obtained for the Robin and Neumann spectral fractional Laplacians. The local decay rates of the solutions are the same for both the Neumann and the Robin problems and are explicitly quantized by a weighted spherical spectral problem with some symmetry.

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Alessandra De Luca, Veronica Felli, Stefano Vita. 2026-07-31. Edge asymptotics for weighted Robin equations on cylinders with applications to spectral fractional Laplacians. https://arxiv.org/abs/2607.29547

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