4 papers
Local boundary conditions in nonlocal hyperelasticity via heterogeneous horizons
Carolin Kreisbeck, Hidde Schönberger
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classi…
-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
This work revolves around the rigorous asymptotic analysis of models in nonlocal hyperelasticity. The corresponding variational problems involve integral functionals depending on n…
Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities
Dominik Engl, Carolin Kreisbeck, Marco Morandotti
Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides…
Non-constant functions with zero nonlocal gradient and their role in nonlocal Neumann-type problems
Carolin Kreisbeck, Hidde Schönberger
This work revolves around properties and applications of functions whose nonlocal gradient, or more precisely, finite-horizon fractional gradient, vanishes. Surprisingly, in contra…