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Sur une famille de variétés à bord lipschitziennes. Application à un problème d'identification de domaines

Denise Chenais — 1977

Annales de l'institut Fourier

$D$ étant un ouvert borné de $R^{n}$ donné, on considère l’ensemble $V L (r, k)$ des ouverts de $R^{n}$ inclus dans $D$ , localement uniformément image de demi-espaces par des homéomorphismes bilipschitiziens. Les cartes locales sont définies sur des boules de rayon $r$ , elles sont bilipschitziennes de constante $k$ . On montre que cette famille est plus générale que celle des ouverts uniformément lipschitziens. On montre ensuite en utilisant une méthode de réflexions que pour $Ω \in V L (r, k)$ , les espaces...

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