BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The positive Jacobian constraint in elasticity theory and orientat
 ion-preserving Young measures - Dr Filip Rindler\, University of Warwick
DTSTART:20151013T130000Z
DTEND:20151013T170000Z
UID:TALK60357@talks.cam.ac.uk
CONTACT:CCA
DESCRIPTION:In elasticity theory\, one naturally requires that the Jacobia
 n determinant of the deformation is positive or even a-priori prescribed (
 for example in the case of incompressibility). However\, such strongly non
 -linear and non-convex constraints are difficult to deal with in mathemati
 cal models. In this minicourse\, I will present various recent results on 
 how this constraint can be manipulated in subcritical Sobolev spaces\, whe
 re the integrability exponent is less than the dimension. This setting is 
 related to cavitation and fracture phenomena in materials. In particular\,
  after introducing the appropriate notions\, I will present a characteriza
 tion of such constraint on the Jacobian determinant formulated in the lang
 uage of Young measures. These objects\, which I will briefly introduce\, a
 re widely used in the Calculus of Variations to model limits of nonlinear 
 functions of weakly converging "generating" sequences. I will also discuss
  relations to  convex integration and "geometry" in matrix space. Finally\
 , I will show some applications to the minimization of integral functional
 s\, the theory of semiconvex hulls and incompressible extensions. 
LOCATION:MR2
END:VEVENT
END:VCALENDAR