In this paper, we will estimate the lower bounds and upper bounds of the first eigenvalues for bi-harmonic operators on manifolds through Reilly's and Bochner's formulae, respectively.
Dans cette Note, nous donnons des minorants et majorants des premières valeurs propres de l'opérateur bi-harmonique sur une variété riemannienne, compacte, connexe, en utilisant respectivement les formules de Reilly et de Bochner.
Accepted:
Published online:
Liuwei Zhang 1
@article{CRMATH_2015__353_8_735_0, author = {Liuwei Zhang}, title = {The lower and upper bounds of the first eigenvalues for the bi-harmonic operator on manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {735--740}, publisher = {Elsevier}, volume = {353}, number = {8}, year = {2015}, doi = {10.1016/j.crma.2015.06.001}, language = {en}, }
Liuwei Zhang. The lower and upper bounds of the first eigenvalues for the bi-harmonic operator on manifolds. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 735-740. doi : 10.1016/j.crma.2015.06.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.001/
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☆ This work is supported by the National Natural Science Foundation of China (No. 11201400).
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