$b$-coercive convolution equations in weighted function spaces and applications
We study the $b$-separability properties of elliptic convolution operators in weighted Besov spaces and establish sharp estimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, in addition, play the role of negative generators of anal...
Збережено в:
| Дата: | 2017 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2017
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1789 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We study the $b$-separability properties of elliptic convolution operators in weighted Besov spaces and establish sharp
estimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, in
addition, play the role of negative generators of analytic semigroups. Moreover, the maximal $b$-regularity properties of
the Cauchy problem for a parabolic convolution equation are established. Finally, these results are applied to obtain the
maximal regularity properties for anisotropic integro-differential equations and the system of infinitely many convolution
equations. |
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