Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces

Korte, Riikka; Lahti, Panu

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 1, pp. 129-154.

Nous étudions l'équivalence entre l'inégalité de Poincaré et plusieurs différentes inégalités isopérimétriques relatives sur les espaces métriques mesurés. Nous utilisons ensuite ces inégalités afin d'établir des conditions suffisantes sur le périmètre fini d'ensembles.

We study equivalence between the Poincaré inequality and several different relative isoperimetric inequalities on metric measure spaces. We then use these inequalities to establish sufficient conditions for the finite perimeter of sets.

Classification : 28A12, 26A45, 30L99

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