Universal inequalities for the eigenvalues of a power of the Laplace operator

Autor:	Ilias, Said, Makhoul, Ola
Rok vydání:	2010
Předmět:	Mathematics - Spectral Theory Mathematics - Differential Geometry 35P15 58C40
Druh dokumentu:	Working Paper
Popis:	In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. This formula generalizes earlier ones obtained by Harrell, Stubbe, Hook, Ashbaugh, Hermi, Levitin and Parnovski. We also show how one can use this abstract formulation both for giving dierent and simpler proofs for all the known results obtained for the eigenvalues of a power of the Laplace operator (i.e. the Dirichlet Laplacian, the clamped plate problem for the bilaplacian and more generally for the polyharmonic problem on a bounded Euclidean domain) and to obtain new ones. In a last paragraph, we derive new bounds for eigenvalues of any power of the Kohn Laplacian on the Heisenberg group. Comment: A para\^itre \`a Manuscripta Mathematica (29 pages)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1001.5102 Zobrazit plný text záznamu View this record from Arxiv