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arXiv · 2006.16672

Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems

Aidyn Kassymov·Michael Ruzhansky·Berikbol T. Torebek
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Abstract

In this paper in the cylindrical domain we consider a fractional elliptic operator with Dirichlet conditions. We prove, that the first eigenvalue of the fractional elliptic operator is minimised in a circular cylinder among all cylindrical domains of the same Lebesgue measure. This inequality is called the Rayleigh-Faber-Krahn inequality. Also, we give Lyapunov and Hartmann-Wintner inequalities for the fractional elliptic boundary value problem.

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Aidyn Kassymov, Michael Ruzhansky, Berikbol T. Torebek. 2020-06-30. Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems. https://doi.org/10.1007/s00009-023-02334-0

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