Real Algebraic and Analytic Geometry |

Dirichlet-regularity in polynomially bounded $o$-minimal structures on IR.

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Submission: 2004, February 11.

*Abstract:
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.

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