Solvability of inhomogeneous boundary-value problems for fourth-order differential equations
We consider a Cauchy-type boundary-value problem of, a problem with three boundary conditions, and the Dirichlet problem for a general fourth-order differential equation with constant complex coefficients and nonzero right-hand side in a bounded domain $\Omega \subset R^2$ with smooth boundary. Us...
Збережено в:
| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2011
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2781 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We consider a Cauchy-type boundary-value problem of, a problem with three boundary conditions,
and the Dirichlet problem for a general fourth-order differential equation with constant complex coefficients
and nonzero right-hand side in a bounded domain $\Omega \subset R^2$ with smooth boundary. Using the method of the Green formula,
the theory of expansion of differential operators, and the theory of $L$-traces (i.e., traces associated with a differential operation $L$), we obtain necessary and sufficient (for elliptic operators)
conditions for the solvability of each of the problems under consideration in the space $H^m(\Omega),\;\; m \geq 4$. |
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