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, p. 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.

@article{AFST_2007_6_16_1_125_0,
     author = {Miranda, Michele, Jr and Pallara, Diego and Paronetto, Fabio and Preunkert, Marc},
     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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 16},
     number = {1},
     year = {2007},
     pages = {125-145},
     doi = {10.5802/afst.1142},
     mrnumber = {2325595},
     zbl = {pre05247242},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2007_6_16_1_125_0}
}
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/item/AFST_2007_6_16_1_125_0/

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