Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866929686671523840 |
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| author | Kassymov, Aidyn Ruzhansky, Michael Torebek, Berikbol T. |
| author_facet | Kassymov, Aidyn Ruzhansky, Michael Torebek, Berikbol T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_16672 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems Kassymov, Aidyn Ruzhansky, Michael Torebek, Berikbol T. Analysis of PDEs Spectral Theory 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. |
| title | Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner inequalities for fractional elliptic problems |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2006.16672 |