Speaker
Dominik Engl
Description
Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this talk, we prove that BV-ellipticity coincides with the simpler notion of biconvexity for a class of densities that depend only on the jump height and jump normal and are positively 1-homogeneous in the first argument. The second main result is the analogous statement in the setting of bounded deformations, where we show that BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily inspired by constructions from the analysis of structured deformations and the general theory of free discontinuity problems. This is joint work with Carolin Kreisbeck and Marco Morandotti.
