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CATEGORIES:Cambridge Centre for Analysis talks
SUMMARY:The positive Jacobian constraint in elasticity the
ory and orientation-preserving Young measures - Dr
Filip Rindler\, University of Warwick
DTSTART;TZID=Europe/London:20151013T140000
DTEND;TZID=Europe/London:20151013T180000
UID:TALK60357AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60357
DESCRIPTION:In elasticity theory\, one naturally requires that
the Jacobian determinant of the deformation is po
sitive or even a-priori prescribed (for example in
the case of incompressibility). However\, such st
rongly non-linear and non-convex constraints are d
ifficult to deal with in mathematical models. In t
his minicourse\, I will present various recent res
ults on how this constraint can be manipulated in
subcritical Sobolev spaces\, where the integrabili
ty exponent is less than the dimension. This setti
ng is related to cavitation and fracture phenomena
in materials. In particular\, after introducing t
he appropriate notions\, I will present a characte
rization of such constraint on the Jacobian determ
inant formulated in the language of Young measures
. These objects\, which I will briefly introduce\,
are widely used in the Calculus of Variations to
model limits of nonlinear functions of weakly conv
erging "generating" sequences. I will also discuss
relations to convex integration and "geometry" i
n matrix space. Finally\, I will show some applica
tions to the minimization of integral functionals\
, the theory of semiconvex hulls and incompressibl
e extensions.
LOCATION:MR2
CONTACT:CCA
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