Translator Disclaimer
1 April 2009 The Dirichlet problem in the plane with semianalytic raw data, quasi analyticity, and o-minimal structure
Tobias Kaiser
Author Affiliations +
Duke Math. J. 147(2): 285-314 (1 April 2009). DOI: 10.1215/00127094-2009-012

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 zero lies in a certain quasi-analytic class used by Ilyashenko [21]–[23] 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 angles at the singular boundary points of the domain are irrational multiples of π

Citation

Download Citation

Tobias Kaiser. "The Dirichlet problem in the plane with semianalytic raw data, quasi analyticity, and o-minimal structure." Duke Math. J. 147 (2) 285 - 314, 1 April 2009. https://doi.org/10.1215/00127094-2009-012

Information

Published: 1 April 2009
First available in Project Euclid: 17 March 2009

zbMATH: 1168.03028
MathSciNet: MR2495077
Digital Object Identifier: 10.1215/00127094-2009-012

Subjects:
Primary: 03C64 , 32B20 , 35J25 , 37E35
Secondary: 30D05 , 30D60 , 30E15 , 35C20

Rights: Copyright © 2009 Duke University Press

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.147 • No. 2 • 1 April 2009
Back to Top