Theorems on isomorphisms for some parabolic initial-boundary-value problems in Hörmander spaces: limiting case
In Hilbert Hörmander spaces, we study the initial-boundary-value problems for arbitrary parabolic differential equations of the second order with Dirichlet boundary conditions or general boundary conditions of the first order in the case where the solutions of these problems belong to the space $H^{...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2016
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1878 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | In Hilbert Hörmander spaces, we study the initial-boundary-value problems for arbitrary parabolic differential equations of
the second order with Dirichlet boundary conditions or general boundary conditions of the first order in the case where the solutions of these problems belong to the space $H^{2,1,\varphi}$. It is shown that the operators corresponding to these problems are
isomorphisms between suitable Hörmander spaces. The regularity of the functions that form these spaces is characterized by a couple of numerical parameters and a functional parameter $\varphi$ slowly varying at infinity in Karamata’s sense. Due to the presence of the parameter $\varphi$, the Hörmander spaces describe the regularity of the functions more precisely than the
anisotropic Sobolev spaces. |
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