Short-time heat flow and functions of bounded variation in R N
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 125-145.

We prove a characterisation of sets with finite perimeter and BV functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

On prouve une caractérisation des ensembles avec périmètre fini et des fonctions à variation bornée en termes du comportement du semi-groupe de la chaleur dans R N au voisinage de t=0. On prouve aussi un résultat plus précis pour les ensembles avec frontière assez régulière.

DOI: 10.5802/afst.1142
Miranda, Michele Jr 1; Pallara, Diego 1; Paronetto, Fabio 1; Preunkert, Marc 2

1 Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy
2 Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany.
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Miranda, Michele Jr; Pallara, Diego; Paronetto, Fabio; Preunkert, Marc. Short-time heat flow and functions of bounded variation in $\mathbf{R}^N$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 1, pp. 125-145. doi : 10.5802/afst.1142. http://www.numdam.org/articles/10.5802/afst.1142/

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