Modul:   MAT673  Seminar PDE and Mathematical Physics

[Video Seminar] Relaxation in nonlinear elasticity

Vortrag von Prof. Dr. Sergio Conti

Datum: 13.11.14  Zeit: 18.10 - 19.10  Raum: Y27H35/36

PDFWe consider vectorial variational problems of the form $E[u]=\int W(Du)$, typical for example of nonlinear elasticity. If $W$ is not quasiconvex then $E$ is not lower semicontinuous and does not, in general, have minimizers. Low-energy states can be studied via the relaxation of $E$. We discuss how, in some situations of physical interest, the relaxation of $E$ can be explicitly characterized. One key difficulty is the inclusion of nonlinear constraints of the form $\det Du=1$ or $\det Du>0$ almost everywhere, which physically represent incompressibility and (local) non-interprenetation of matter. This talk is based on joint work with Georg Dolzmann.