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

Michele Miranda; Diego Pallara; Fabio Paronetto; Marc Preunkert — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

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.

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Short-time heat flow and functions of bounded variation in R N

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