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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Lower semicontinuity for minimization problems in
the space BD of functions of bounded deformation -
Filip Rindler (Cambridge)
DTSTART;TZID=Europe/London:20111114T160000
DTEND;TZID=Europe/London:20111114T170000
UID:TALK34506AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/34506
DESCRIPTION:This talk considers minimization problems for inte
gral functionals on the linear-growth space BV of
functions of bounded variation and on the space BD
of functions of bounded deformation. The space BD
consists of all L^1^-functions\, whose distributi
onal symmetrized derivative (defined by duality wi
th the symmetrized gradient (\\nabla u + \\nabla u
^T^)/2) is representable as a finite Radon measure
. Such functions play an important role in a varie
ty of variational models involving (linear) elasto
-plasticity. In this talk\, I will present the fir
st general lower semicontinuity theorem for integr
al functionals with linear growth on the space BD
under the (natural) assumption of symmetric-quasic
onvexity. This establishes the existence of soluti
ons to a class of minimization problems in which f
ractal phenomena may occur. The proof proceeds via
generalized Young measures and a construction of
good blow-ups\, based on local rigidity/ellipticit
y arguments for some differential inclusions. A si
milar strategy also allows to give a proof of the
classical lower semicontinuity theorem in BV for q
uasiconvex integral functionals without invoking A
lberti's Rank-One Theorem.
LOCATION:CMS\, MR15
CONTACT:Jonathan Ben-Artzi
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