Estimates of eigenvalues of an elliptic differential system in divergence form
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Publication:6354668
DOI10.1007/S00033-022-01848-ZarXiv2011.13507WikidataQ114231765 ScholiaQ114231765MaRDI QIDQ6354668
José. N. V. Gomes, Marcio Costa Araújo Filho
Publication date: 26 November 2020
Abstract: In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity inequalities of the eigenvalues of the Laplacian, more precisely, we consider a countable family of bounded domains in Gaussian shrinking soliton that makes the behavior of known estimates of the eigenvalues of the Laplacian invariant by a first-order perturbation of the Laplacian. We also address the Gaussian expanding soliton case in two different settings. We finish with the special case of divergence-free tensors which is closely related to the Cheng-Yau operator.
Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) General theory of partial differential operators (47F05) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Rigidity results (53C24)
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