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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Dirichlet regularity of subanalytic domains
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by Tobias Kaiser PDF
Trans. Amer. Math. Soc. 360 (2008), 6573-6594 Request permission


Let ${\Omega }$ be a bounded and subanalytic domain in ${{\mathbb R}^n}$, ${n \geq 2}$. We show that the set of boundary points of ${\Omega }$ which are regular with respect to the Dirichlet problem is again subanalytic. Moreover, we give sharp upper bounds for the dimension of the set of irregular boundary points. This enables us to decide whether the domain has a classical Green function. In dimensions 2 and 3, this is the case, given some mild and necessary conditions on the topology of the domain.
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Additional Information
  • Tobias Kaiser
  • Affiliation: Naturwissenschaftliche Fakultät-Mathematik, University of Regensburg, Universitätsstr. 31, 93040 Regensburg, Germany
  • MR Author ID: 684790
  • Email:
  • Received by editor(s): March 23, 2006
  • Received by editor(s) in revised form: February 5, 2007
  • Published electronically: July 22, 2008
  • Additional Notes: This research was supported by DFG-Projekt KN202/5-1
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 6573-6594
  • MSC (2000): Primary 31B25, 32B20; Secondary 03C64
  • DOI:
  • MathSciNet review: 2434300