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 of the Dirichlet solution at a boundary point with angle greater than zero lies in a certain quasi-analytic class used by Ilyashenko [21] - [23] in his work on Hilbert's PF 16th problem. With this result we can prove that the ...
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 of the Dirichlet solution at a boundary point with angle greater than zero lies in a certain quasi-analytic class used by Ilyashenko [21] - [23] in his work on Hilbert's PF 16th problem. With this result we can prove that the Dirichlet solution is definable in an o-minimal structure if the angles at the singular boundary points of the domain arc, irrational multiples of pi.
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