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Winter 2002 John functions, quadratic integral forms and o-minimal structures
K. Kurdyka, J. Xiao
Illinois J. Math. 46(4): 1089-1109 (Winter 2002). DOI: 10.1215/ijm/1258138468

Abstract

Let $\Omega$ be a proper subdomain of $\mathbb{R}^n$, $n\ge 2$, and let $\partial{\Omega}$ and $\delta_{\Omega}(x)$ denote, respectively, the boundary of $\Omega$ and the Euclidean distance of the point $x\in \Omega$ to $\mathbb{R}^n \setminus\Omega$. Denote by $K(\Omega)$ the John space of all $C^1$ functions $f:\Omega\rightarrow\mathbb{R}$ with $\sup_{x\in \Omega}\delta_\Omega (x)|\nabla f(x)|<+\infty$. We study $K(\Omega)$-functions via quadratic integral forms and o-minimal structures.

Citation

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K. Kurdyka. J. Xiao. "John functions, quadratic integral forms and o-minimal structures." Illinois J. Math. 46 (4) 1089 - 1109, Winter 2002. https://doi.org/10.1215/ijm/1258138468

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1040.31004
MathSciNet: MR1988252
Digital Object Identifier: 10.1215/ijm/1258138468

Subjects:
Primary: 32B20
Secondary: 14P15, 31B05, 31B10

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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