On the Dirichlet problem for A-harmonic functions





A-harmonic equations, degenerate Beltrami equations, BMO, bounded mean oscillation, FMO, finite mean oscillation, Dirichlet problem, potential theory


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 £ 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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Gutlyanskii, V., Ryazanov, V., Sevost’yanov, E. & Yakubov, E. (2023). Hydrodynamic normalization in the theory of degenerate Beltrami equations. Dopov. Nac. akad. nauk Ukr., No. 2, pp. 10-17. https://doi.org/10.15407/ dopovidi2023.02.010

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How to Cite

Gutlyanskiĭ, V., Ryazanov, V., Sevost’yanov, E., & Yakubov, E. (2023). On the Dirichlet problem for A-harmonic functions. Reports of the National Academy of Sciences of Ukraine, (4), 11–19. https://doi.org/10.15407/dopovidi2023.04.011