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Short-time heat flow and functions of bounded variation in R N
Michele Miranda1; Diego Pallara1; Fabio Paronetto1; Marc Preunkert2
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.
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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1142

Michele Miranda 1; Diego Pallara 1; Fabio Paronetto 1; Marc Preunkert 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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Michele Miranda; Diego Pallara; Fabio Paronetto; Marc Preunkert. 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

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