Elliptic Boundary-Value Problems in the Sense of Lawruk on Sobolev and Hörmander Spaces
We study elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to a problem of this kind is bounded and Fredholm in appropriate couples of the inner product isotropic Hörmander spa...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2015
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/2014 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We study elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to a problem of this kind is bounded and Fredholm in appropriate couples of the inner product isotropic Hörmander spaces $H^{s,φ}$, which form the refined Sobolev scale. The order of differentiation for these spaces is given by a real number $s$ and a positive function $φ$ slowly varying at infinity in Karamata’s sense.
We consider this problem for an arbitrary elliptic equation $Au = f$ in a bounded Euclidean domain $Ω$ under the condition that $u ϵ H^{s,φ} (Ω),\; s < \text{ord} A$, and $f ϵ L_2 (Ω)$. We prove theorems on the a priori estimate and regularity of the generalized solutions to this problem. |
|---|