Kaiser, Tobias (2009) THE DIRICHLET PROBLEM IN THE PLANE WITH SEMIANALYTIC RAW DATA, QUASI ANALYTICITY, AND O-MINIMAL STRUCTURE. DUKE MATHEMATICAL JOURNAL, 147 (2). pp. 285-314. ISSN 0012-7094,
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | EXPONENTIAL FUNCTION; SUBANALYTIC SETS; PFAFFIAN SETS; FIELD; CLASSIFICATION; NUMBERS; SERIES; PAIRS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Sep 2020 08:59 |
| Last Modified: | 18 Sep 2020 08:59 |
| URI: | https://pred.uni-regensburg.de/id/eprint/29155 |
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