On the Dirichlet problem for A-harmonic functions
Vladimir Ya. Gutlyanskiĭ, Vladimir I. Ryazanov, Evgeny Sevost’yanov, Eduard Yakubov · Reports of the National Academy of Sciences of Ukraine · 2023
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.