A Dirichlet Problem For Generalized Analytic Functions


Abstract


For the existence of the solution for the Dirichlet Problem\[\frac{\partial w}{\partial \overline{z}}=-(Aw+B\overline{w}),\quad z\in D\]\[Rew|_{\partial D}=g,\quad g\in C^{\alpha }(\partial D)\]\[Imw(z_{0})=c_{0},\quad z_{0}\in \overline{D}\]\noindent in a domain having a smooth boundary \(D\subset C\), necessaryconditions are studied. Here we assumed that \(z\in D\), \(g\in C^{\alpha}(\partial D)\), \(z_{0}\in {\overline{D}}\) and \(A,B\in C^{\alpha }(\overline{D})\).

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