Calculus of Variations and Geometric Measure Theory
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M. Miranda Jr - D. Pallara - F. Paronetto - M. Preunkert

On a characterisation of perimeters in $\Bbb R^N$ via heat semigroup

created by miranda on 20 Feb 2008
modified by root on 09 Oct 2011


Published Paper

Inserted: 20 feb 2008
Last Updated: 9 oct 2011

Journal: Ricerche Mat.
Volume: 54
Number: 2
Pages: 615-621
Year: 2006


In this poster we present the results contained in \cite{MirPalParPre04}; in that paper we generalise to all sets with finite perimeter an equality concerning the short time behaviour of the heat semigroup proved for balls in \cite{Led94} and exploited there in connection with the isoperimetric inequality. For sets with smooth boundary a more precise result is shown. \noindent The above result for sets with finite perimeter gives also a characterization of the perimeter using the heat semigroup very similar to the one used by De Giorgi in \cite{DG54} to define the perimeter. We also extend these results to all the function with bounded variation, giving a relation between the jump part of the total variation measure and the small time diffusion of the level sets.


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