We consider some boundary behavior effect for bianalytic functions related to the Dirichlet problem solvability. It is proved that there exist such Jordan domains (even with infinitely smooth but not analytic boundaries) where non-constant bianalytic functions may can tend to zero near the boundary only sufficiently slow. More precisely, we prove that for any \(\alpha \) and \(\beta \) such that \(0<\alpha<\beta <1\), there exists a Jordan domain \(D=D(\alpha ,\beta )\) possessing the following two properties: (i) there exists a non-constant function of the class \({\mathrm {Lip}}_\alpha ({{\overline{D}}})\) which is bianalytic in D and vanishes identically on the boundary \(\partial D\) of D; (ii) every arc containing in \(\partial D\) is a uniqueness set for functions bianalytic in D and belonging to the class \({\mathrm {Lip}}_\beta ({{\overline{D}}})\).

我们考虑与狄利克雷问题的可解性相关的双分析函数的一些边界行为效应。已证明存在这样的 Jordan 域（即使具有无限平滑但不是解析边界），其中非常数双解析函数可能在边界附近趋于零，但速度足够慢。更准确地说，我们证明对于任何\(\alpha \)和\(\beta \)使得\(0<\alpha<\beta <1\)，存在一个 Jordan 域\(D=D(\alpha ,\beta )\)具有以下两个性质： (i) 存在类\({\mathrm {Lip}}_\alpha ({{\overline{D}}})\)的非常量函数在D中是偏析的并且在边界上完全消失\(\partial D\)的D ; (ii) \(\partial D\) 中包含的每条弧都是D 中双分析函数的唯一集，属于类\({\mathrm {Lip}}_\beta ({{\overline{D}}} )\)。