Short-time heat flow and functions of bounded variation in $\mathbf{R}^N$

Miranda, Michele Jr; Pallara, Diego; Paronetto, Fabio; Preunkert, Marc

doi:10.5802/afst.1142

Short-time heat flow and functions of bounded variation in

R^{N}

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.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 16 (2007) no. 1, pp. 125-145.

Résumé
Abstract

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.

We prove a characterisation of sets with finite perimeter and $B V$ 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.

DOI : 10.5802/afst.1142

Affiliations des auteurs :

Miranda, Michele Jr ¹ ; Pallara, Diego ¹ ; Paronetto, Fabio ¹ ; Preunkert, Marc ²

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     title = {Short-time heat flow and functions of bounded variation in $\mathbf{R}^N$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {125--145},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
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     url = {http://www.numdam.org/articles/10.5802/afst.1142/}
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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, Série 6, Tome 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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