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arXiv · 2604.01895

Sharp spectral estimates for free boundary problems arising in plasma physics

Daniele Bartolucci·Aleks Jevnikar·Juncheng Wei·Ruijun Wu
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Abstract

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 $\sigma_1$, 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 $\sigma_1$ is always positive. The implications about the uniqueness problem for the Emden equation are also discussed.

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Daniele Bartolucci, Aleks Jevnikar, Juncheng Wei, Ruijun Wu. 2026-04-02. Sharp spectral estimates for free boundary problems arising in plasma physics. https://doi.org/10.57262/die039-1112-935

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