John functions, quadratic integral forms and o-minimal structures
Kurdyka, K. ; Xiao, J.
Illinois J. Math., Tome 46 (2002) no. 3, p. 1089-1109 / Harvested from Project Euclid
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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.
Publié le : 2002-10-15
Classification:  32B20,  14P15,  31B05,  31B10 
@article{1258138468,
     author = {Kurdyka, K. and Xiao, J.},
     title = {John functions, quadratic integral forms and o-minimal structures},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 1089-1109},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138468}
}

Kurdyka, K.; Xiao, J. John functions, quadratic integral forms and o-minimal structures. Illinois J. Math., Tome 46 (2002) no. 3, pp.  1089-1109. http://gdmltest.u-ga.fr/item/1258138468/