Kaiser, Tobias (2006) Dirichlet regularity in arbitrary o-minimal structures on the field R up to dimension 4. MATHEMATISCHE NACHRICHTEN, 279 (15). pp. 1669-1683. ISSN 0025-584X,
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In this article we show that the set of Dirichlet regular boundary points of a bounded domain of dimension up to 4, definable in an arbitrary o-minimal structure on the field R, is definable in the same structure. Moreover we give estimates for the dimension of the set of non-regular boundary points, depending on whether the structure is polynomially bounded or not. This paper extends the results from the author's Ph.D. thesis [6, 7] where the problem was solved for polynomially bounded o-minimal structures expanding the real field. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; o-minimal structures; Dirichlet problem |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Mar 2021 09:35 |
| Last Modified: | 03 Mar 2021 09:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/35225 |
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