Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients
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...
Збережено в:
| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/166240 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 eigenvalues. Moreover, we also obtain estimates for some special cases of this problem. In particular, our results generalize the Wang -Xia inequality (J. Funct. Anal. - 2007. - 245) for the clamped plate problem to a fourth-order elliptic operator with variable coefficients. |
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