Sharp spectral estimates for free boundary problems arising in plasma physics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908933441978368 |
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| author | Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun |
| author_facet | Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun |
| contents | We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analysis of a non-local eigenvalue equation. Consequently the corresponding first eigenvalue, say $σ_1$, is not a standard one and it is shown that it cannot satisfy a general isoperimetric property of Faber-Krahn type. This motivates a careful analysis of the problem on balls in any dimension $N\geq 2$, where we prove that in fact $σ_1$ is always positive. The implications about the uniqueness problem for the Emden equation are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01895 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp spectral estimates for free boundary problems arising in plasma physics Bartolucci, Daniele Jevnikar, Aleks Wei, Juncheng Wu, Ruijun Analysis of PDEs 35B09, 35B32, 35J61, 35Q99, 35R35, 82D10 We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analysis of a non-local eigenvalue equation. Consequently the corresponding first eigenvalue, say $σ_1$, is not a standard one and it is shown that it cannot satisfy a general isoperimetric property of Faber-Krahn type. This motivates a careful analysis of the problem on balls in any dimension $N\geq 2$, where we prove that in fact $σ_1$ is always positive. The implications about the uniqueness problem for the Emden equation are also discussed. |
| title | Sharp spectral estimates for free boundary problems arising in plasma physics |
| topic | Analysis of PDEs 35B09, 35B32, 35J61, 35Q99, 35R35, 82D10 |
| url | https://arxiv.org/abs/2604.01895 |