V.Ya. Gutlyanskiĭ, V.I. Ryazanov, E.A. Sevost’yanov, E. Yakubov
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引用次数: 0
摘要
研究了无边界分量退化为单点的复平面£的任意有界域D上A-调和方程div[A grad u] = 0具有连续边界数据的Dirichlet边值问题。我们给出了问题弱解存在的积分判据，包括用A (z)表示的BMO和FMO判据。我们还讨论了a -调和函数与势理论之间的联系。
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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