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 (2007)

  • Volume: 16, Issue: 1, page 125-145
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Miranda, Michele, et al. "Short-time heat flow and functions of bounded variation in $\mathbf{R}^N$." Annales de la faculté des sciences de Toulouse Mathématiques 16.1 (2007): 125-145. <http://eudml.org/doc/10026>.

@article{Miranda2007,
abstract = {We prove a characterisation of sets with finite perimeter and $BV$ functions in terms of the short time behaviour of the heat semigroup in $\{\bf R\}^N$. For sets with smooth boundary a more precise result is shown.},
affiliation = {Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy; Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy; Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy; Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany.},
author = {Miranda, Michele, Pallara, Diego, Paronetto, Fabio, Preunkert, Marc},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {heat semigroup in },
language = {eng},
number = {1},
pages = {125-145},
publisher = {Université Paul Sabatier, Toulouse},
title = {Short-time heat flow and functions of bounded variation in $\mathbf\{R\}^N$},
url = {http://eudml.org/doc/10026},
volume = {16},
year = {2007},
}

TY - JOUR
AU - Miranda, Michele
AU - Pallara, Diego
AU - Paronetto, Fabio
AU - Preunkert, Marc
TI - Short-time heat flow and functions of bounded variation in $\mathbf{R}^N$
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2007
PB - Université Paul Sabatier, Toulouse
VL - 16
IS - 1
SP - 125
EP - 145
AB - We prove a characterisation of sets with finite perimeter and $BV$ functions in terms of the short time behaviour of the heat semigroup in ${\bf R}^N$. For sets with smooth boundary a more precise result is shown.
LA - eng
KW - heat semigroup in
UR - http://eudml.org/doc/10026
ER -

References

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  9. E.H. Lieb, M. Loss.— Analysis, Second edition, Amer. Math. Soc., 2001 Zbl0966.26002MR1817225
  10. M. Miranda (Jr), D. Pallara, F. Paronetto, M. Preunkert.— Heat Semigroup and B V Functions on Riemannian Manifolds, forthcoming. 
  11. K. Pietruska-Paluba.— Heat kernels on metric spaces and a characterisation of constant functions, Manuscripta Math. 115 , p. 389–399 (2004). Zbl1062.60076MR2102059
  12. M. Preunkert.— A semigroup version of the isoperimetric inequality, Semigroup Forum 68, p. 233-245 (2004). Zbl1093.47042MR2036625
  13. M. H. Taibleson.— On the theory of Lipschitz spaces of distributions on Euclidean n -spaces I, J. Math. Mech. 13, p. 407-479 (1964). Zbl0132.09402MR163159
  14. H. Triebel.— Interpolation theory, function spaces, differential operators, North-Holland 1978. Zbl0387.46032MR503903
  15. J. Wloka.— Partial Differential Equations, Cambridge U. P., 1987. Zbl0623.35006MR895589

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