Псевдодиференціальні рівняння та альфа-стійкі випадкові процеси
The notion of a single-layer potential for a class of pseudodifferential equations associated with rotationally invariant $\alpha$-stable stochastic processes is introduced. A certaine analogy to the classical theorem on the jump of the conormal derivative of a single-layer potential is established....
Збережено в:
| Дата: | 2022 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/508 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| Резюме: | The notion of a single-layer potential for a class of pseudodifferential equations associated with rotationally invariant $\alpha$-stable stochastic processes is introduced. A certaine analogy to the classical theorem on the jump of the conormal derivative of a single-layer potential is established. This result makes it possible to construct fundamental solutions of some initial-boundary value problems for the equations mentioned above. A probabilistic interpretation of those solutions is presented. The results of investigations on the topic published by the authors during 2014--2018 are expounded in this article in a systematized and modified form. |
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