Abstract for the talk on 08.12.2017 (11:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Johannes Diermeier (Universität Bonn)
Korn-Poincaré-type inequalities and energy density for a subspace of SBDp
Specialized functions of bounded deformation are established as an setting for elasticity problems in which deformations are allowed to jump on some (n − 1)-dimensional set. We are interested in a speciﬁc subspace of these functions (in 2d), in which we ﬁx the possible direction of the jump set for each component. In this setting we are able to provide diﬀerent Korn-Poincaré-type estimates, independent of the size of the jump set. We apply these estimates to approximate such functions with functions that are smooth up to a jump set of ﬁnitely many segments and that satisfy the same directionally constraint.