Моногенні функції в комутативних алгебрах і еліптичні рівняння математичної фізики
An algebraic-analytic approach to elliptic equations of mathe- matical physics is developed at the Department of Complex Analysis and Potential Theory of the Institute of Mathematics of the National Academy of Sciences of Ukraine. This approach means a finding of commutative Ba- nach algebra such tha...
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| Datum: | 2022 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут математики НАН України
2022
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/497 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | An algebraic-analytic approach to elliptic equations of mathe- matical physics is developed at the Department of Complex Analysis and Potential Theory of the Institute of Mathematics of the National Academy of Sciences of Ukraine. This approach means a finding of commutative Ba- nach algebra such that differentiable in the sense of Gâteaux functions with values in this algebra have components satisfying the given equation with par- tial derivatives. Such algebras are found for the biharmonic equation and the three-dimensional Laplace equation and elliptic equations degenerating on an axis that describe axial-symmetric potential fields. An use of differentiable in the sense of Gâteaux functions given in commutative Banach algebras com- bines the preservation of basic properties of analytic functions of a complex variable for the mentioned differentiable functions and the convenience and the simplicity of construction of solutions of PDEs. |
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