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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2012

Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold

Résumé

We establish inequalities for the eigenvalues of the sub-Laplace operator associated with a pseudo-Hermitian structure on a strictly pseudoconvex CR manifold. Our inequalities extend those obtained by Niu and Zhang \cite{NiuZhang} for the Dirichlet eigenvalues of the sub-Laplacian on a bounded domain in the Heisenberg group and are in the spirit of the well known Payne-P\'{o}lya-Weinberger and Yang universal inequalities.
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Dates et versions

hal-00779283 , version 1 (28-01-2013)

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Amine Aribi, Ahmad El Soufi. Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold. Calculus of Variations and Partial Differential Equations, 2012, 47 (3-4), pp.437-463. ⟨10.1007/s00526-012-0523-2⟩. ⟨hal-00779283⟩
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