On the Compactness of One Class of Solutions for the Dirichlet Problem
We consider the Dirichlet problem for the Beltrami equation in an arbitrary bounded simply connected domain in the complex plane $\mathbb {C}$. Namely, we study the class of all regular solutions of such a problem with a normalization condition and set-theoretic constraints on their complex characte...
Збережено в:
| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1054 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | We consider the Dirichlet problem for the Beltrami equation in an arbitrary bounded simply connected domain in the complex plane $\mathbb {C}$. Namely, we study the class of all regular solutions of such a problem with a normalization condition and set-theoretic constraints on their complex characteristics. We have proved the compactness of this class in terms of prime ends for an arbitrary continuous function in the Dirichlet condition.
Mathematical Subject Classification 2020: 30C65, 35J70
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