Mathematics – Analysis of PDEs
Scientific paper
2010-08-12
Mathematics
Analysis of PDEs
48 pages, 3 figures (revised version)
Scientific paper
We establish a general weak* lower semicontinuity result in the space $\BD(\Omega)$ of functions of bounded deformation for functionals of the form $$\Fcal(u) := \int_\Omega f \bigl(x, \Ecal u \bigr) \dd x + \int_\Omega f^\infty \Bigl(x, \frac{\di E^s u}{\di \abs{E^s u}} \Bigr) \dd \abs{E^s u} + \int_{\partial \Omega} f^\infty \bigl(x, u|_{\partial \Omega} \odot n_\Omega \bigr) \dd \Hcal^{d-1}$$, $u \in \BD(\Omega)$. The main novelty is that we allow for non-vanishing Cantor-parts in the symmetrized derivative $Eu$. The proof is accomplished via Jensen-type inequalities for generalized Young measures and a construction of good blow-ups, which is based on local rigidity arguments for some differential inclusions involving symmetrized gradients. This strategy allows us to establish the lower semicontinuity result without an Alberti-type theorem in $\BD(\Omega)$, which is not available at present. We also include existence and relaxation results for variational problems in $\BD(\Omega)$, as well as a complete discussion of some differential inclusions for the symmetrized gradient in two dimensions.
No associations
LandOfFree
Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587094