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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium

Filip Rindler
OxPDE, University of Oxford
Title: Lower semicontinuity and Young measures in BD

Abstract: We establish a general weak star lower semicontinuity result in the space BD of functions of bounded deformation for linear growth functionals. The main novelty is that we allow for a non vanishing Cantor part in the symmetrized derivative. The proof is accomplished via Jensenty inequalities for generalized Young measures and a construction of good blowups, which is based on local rigidity arguments for some underdetermined PDEs involving symmetrized gradients. This strategy allows us to prove the lower semicontinuity result without an Alberti type theorem in BD, which is not available at present. A similar strategy also allows to prove lower semicontinuity in BV without the use of the Alberti Rank One Theorem.

Date: Tuesday, October 5, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  David Kinderlehrer