Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients

• Published in: Український математичний журнал
• Date: 2011
• Main Author: He-Jun Sun
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/166240
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients / He-Jun Sun // Український математичний журнал. — 2011. — Т. 63, № 7. — С. 999–1008. — Бібліогр.: 20 назв. — англ.

We investigate the Dirichlet weighted eigenvalue problem for a fourth-order elliptic operator with variable coefficients in a bounded domain in Rⁿ. We establish a sharp inequality for its eigenvalues. It yields an estimate for the upper bound of the (k+1)-th eigenvalue in terms of the first k eigenv...