The Hausdorff lower semicontinuous envelope of the length in the plane

Raphaël Cerf

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 1, page 33-71
  • ISSN: 0391-173X

Abstract

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We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.

How to cite

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Cerf, Raphaël. "The Hausdorff lower semicontinuous envelope of the length in the plane." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.1 (2002): 33-71. <http://eudml.org/doc/84467>.

@article{Cerf2002,
abstract = {We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.},
author = {Cerf, Raphaël},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {residual domain; Hausdorff measure; 1-set; surface energy; phase coexistence phenomena},
language = {eng},
number = {1},
pages = {33-71},
publisher = {Scuola normale superiore},
title = {The Hausdorff lower semicontinuous envelope of the length in the plane},
url = {http://eudml.org/doc/84467},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Cerf, Raphaël
TI - The Hausdorff lower semicontinuous envelope of the length in the plane
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 1
SP - 33
EP - 71
AB - We study the Hausdorff lower semicontinuous envelope of the length in the plane. This envelope is taken with respect to the Hausdorff metric on the space of the continua. The resulting quantity appeared naturally as the rate function of a large deviation principle in a statistical mechanics context and seems to deserve further analysis. We provide basic simple results which parallel those available for the perimeter of Caccioppoli and De Giorgi.
LA - eng
KW - residual domain; Hausdorff measure; 1-set; surface energy; phase coexistence phenomena
UR - http://eudml.org/doc/84467
ER -

References

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