具有半解析原始数据、拟解析性和o-极小结构的平面上的狄利克雷问题
The Dirichlet problem in the plane with semianalytic raw data, quasianalyticity and o-minimal structures
摘要：
研究了平面上半解析有界区域边界上半解析连续函数的Dirichlet解。我们表明，胚芽的Dirichlet解决方案在边界点与角度大于0在于在一定的准解析类使用的Ilyashenko在他的工作希尔伯特的第16个问题。利用这一结果，我们可以证明：如果区域的奇异边界点处的角是$π$的无理倍，则Dirichlet解在o-极小结构中是可定义的.
英文摘要：
We investigate the Dirichlet solution for a semianalytic continuous function on the boundary of a semianalytic bounded domain in the plane. We show that the germ of the Dirichlet solution at a boundary point with angle greater than 0 lies in a certain quasianalytic class used by Ilyashenko in his work on Hilbert's 16th problem. With this result we can prove that the Dirichlet solution is definable in an o-minimal structure if the angle at a singular boundary point of the domain is an irrational multiple of $π$.
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