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arXiv · 0705.1926

The Dirichlet problem in the plane with semianalytic raw data, quasianalyticity and o-minimal structures

Tobias Kaiser
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Abstract

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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Tobias Kaiser. 2008-07-21. The Dirichlet problem in the plane with semianalytic raw data, quasianalyticity and o-minimal structures. https://arxiv.org/abs/0705.1926

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