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

Michele Miranda; Diego Pallara; Fabio Paronetto; Marc Preunkert

doi:10.5802/afst.1142

Short-time heat flow and functions of bounded variation in

R^{N}

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.

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

Abstract
Abstract

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.

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.

MR

DOI: 10.5802/afst.1142

Author's affiliations:

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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     author = {Michele Miranda and Diego Pallara and Fabio Paronetto and Marc Preunkert},
     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},
     address = {Toulouse},
     volume = {Ser. 6, 16},
     number = {1},
     year = {2007},
     doi = {10.5802/afst.1142},
     mrnumber = {2325595},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1142/}
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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. https://afst.centre-mersenne.org/articles/10.5802/afst.1142/

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