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SUMMARY:Lower semicontinuity for minimization problems in the space BD of 
 functions of bounded deformation - Filip Rindler (Cambridge)
DTSTART:20111114T160000Z
DTEND:20111114T170000Z
UID:TALK34506@talks.cam.ac.uk
CONTACT:Jonathan Ben-Artzi
DESCRIPTION:This talk considers minimization problems for integral functio
 nals on the linear-growth space BV of functions of bounded variation and o
 n the space BD of functions of bounded deformation. The space BD consists 
 of all L^1^-functions\, whose distributional symmetrized derivative (defin
 ed by duality with the symmetrized gradient (\\nabla u + \\nabla u^T^)/2) 
 is representable as a finite Radon measure. Such functions play an importa
 nt role in a variety of variational models involving (linear) elasto-plast
 icity. In this talk\, I will present the first general lower semicontinuit
 y theorem for integral functionals with linear growth on the space BD unde
 r the (natural) assumption of symmetric-quasiconvexity. This establishes t
 he existence of solutions to a class of minimization problems in which fra
 ctal phenomena may occur. The proof proceeds via generalized Young measure
 s and a construction of good blow-ups\, based on local rigidity/ellipticit
 y arguments for some differential inclusions. A similar strategy also allo
 ws to give a proof of the classical lower semicontinuity theorem in BV for
  quasiconvex integral functionals without invoking Alberti's Rank-One Theo
 rem.
LOCATION:CMS\, MR15
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