Real Algebraic and Analytic Geometry

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86. Tobias Kaiser:
Dirichlet-regularity in polynomially bounded $o$-minimal structures on IR.


Submission: 2004, February 11.

Let ${\scriptstyle \Omega\, \subset\, {\mathbb R}^n}$, ${\scriptstyle n\, \geq \, 2}$, be a bounded region definable in a polynomially bounded ${\scriptstyle o}$-minimal structure on ${\scriptstyle {\mathbb R}}$. We show that the set of regular boundary points of ${\scriptstyle \Omega}$ in the sense of Dirichlet is definable in the same ${\scriptstyle o}$-minimal structure.

Mathematics Subject Classification (2000): 03C64, 14P15, 31B15, 35J25.

Keywords and Phrases: Dirichlet-regularity, polynomially bounded $o$-minimal structures.

Full text, 32p.: ps.gz 251k, pdf 284k.

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