Some results on the eigenvalue problem for a fractional elliptic equation
Abstract This paper deals with the eigenvalue problem for a fractional variable coefficients elliptic equation defined on a bounded domain. Compared to the previous work, we prove a quite different variational formulation of the first eigenvalue for the above problem. This allows us to give a variat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1127-y |
| Summary: | Abstract This paper deals with the eigenvalue problem for a fractional variable coefficients elliptic equation defined on a bounded domain. Compared to the previous work, we prove a quite different variational formulation of the first eigenvalue for the above problem. This allows us to give a variational proof of the fractional Faber–Krahn inequality by employing suitable rearrangement techniques. |
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| ISSN: | 1687-2770 |