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Prescription du spectre de Steklov dans une classe conforme

Abstract : On any compact manifold of dimension $n\geq3$ with boundary, we prescibe any finite part of the Steklov spectrum whithin a given conformal class. In particular, we prescribe the multiplicity of the first eigenvalues. On a compact surface with boundary, we show that the multiplicity of the $k$-th eigenvalue is bounded independently of the metric. On the disk, we give more precise results : the multiplicity of the first and second positive eigenvalues are at most 2 and 3 respectively. For the Steklov-Neumann problem on the disk, we prove that the multiplicity of the $k$-th positive eigenvalue is at most $k+1$.
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https://hal.archives-ouvertes.fr/hal-00769259
Contributor : Pierre Jammes <>
Submitted on : Sunday, December 30, 2012 - 2:38:16 PM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM

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Pierre Jammes. Prescription du spectre de Steklov dans une classe conforme. Analysis & PDE, Mathematical Sciences Publishers, 2014, 7 (3), pp.529-550. ⟨10.2140/apde.2014.7.529⟩. ⟨hal-00769259⟩

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