On the Dirichlet problem for A-harmonic functions
We study the Dirichlet boundary value problem with continuous boundary data for the A-harmonic equations div[A grad u] = 0 in an arbitrary bounded domain D of the complex plane С with no boundary component degenerated to a single point. We provide integral criteria, including the BMO and FMO criteri...
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| Date: | 2019 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Видавничий дім "Академперіодика" НАН України
2019
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| Series: | Вісник НАН України |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Dirichlet problem for A-harmonic functions / V.Ya. Gutlyanskiĭ, V.I. Ryazanov, E.A. Sevost’yanov, E.Yakubov // Доповіді Національної академії наук України. — 2023. — № 4. — С. 11-19. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We study the Dirichlet boundary value problem with continuous boundary data for the A-harmonic equations div[A grad u] = 0 in an arbitrary bounded domain D of the complex plane С with no boundary component degenerated to a single point. We provide integral criteria, including the BMO and FMO criteria expressed in terms of A (z), for the existence of weak solutions to the problem. We also discuss the connections between A-harmonic functions and potential theory. |
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