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SUMMARY:Sur l'approximation champ de phase des problĂ¨mes variationnels fa
isant intervenir des ensembles connexes 1D/On a phase-field approximation
of variational problems involving 1D-connected sets
DTSTART;VALUE=DATE-TIME:20180425T083000Z
DTEND;VALUE=DATE-TIME:20180425T093000Z
DTSTAMP;VALUE=DATE-TIME:20200813T172956Z
UID:indico-contribution-1818@indico.math.cnrs.fr
DESCRIPTION:Speakers: Antoine Lemenant (U. Paris-Diderot\, France)\nIt is
nowadays classical that phase transition models such as the Cahn-Hilliard
energy can be used to regularize some more delicate functionals of geometr
ic nature such as the Perimeter functional or more generally the $(N-1)$-H
ausdorff measure. This procedure is sometimes called a Phase-Field method
in numerical analysis and has been used in order to approximate some class
ical shape optimization problems or free discontinuity problems arising in
the calculus of variations. In this talk I will present an elementary way
to constraint the connectedness of the unknown set in the phase-field app
roach. This applies for instance to the so-called Steiner Problem\, for wh
ich we indeed get a phase-field approximation\, but also to other minimizi
ng functionals on which a connectedness constraint is added. This new appr
oach give rise to some interesting mathematical problems\, both from the t
heoretical point of view than from the numerical one.\n\nhttps://indico.ma
th.cnrs.fr/event/3052/contributions/1818/
LOCATION:
URL:https://indico.math.cnrs.fr/event/3052/contributions/1818/
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