4 citations · 6 across the 6 of their papers we have counts for
7 papers
Formation of shear bands through discrete localized plastic increments
Heiner Olbermann, Hidde Schönberger
We study rate-independent systems in which the evolution is obtained by incremental minimization of elastic energy and one-homogeneous dissipation under constraints on the admissib…
From plans to maps: Nonlocal regularization of optimal transport
Marcello Carioni, Leonardo Del Grande, José A. Iglesias +1
We introduce a nonlocal regularization of optimal transport that bridges Kantorovich and Monge formulations. The regularization penalizes oscillations through an interaction kernel…
-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…
Nonlocal gradients: Fundamental theorem of calculus, Poincaré inequalities and embeddings
José Carlos Bellido, Carlos Mora-Corral, Hidde Schönberger
We address the study of nonlocal gradients defined through general radial kernels . Our investigation focuses on the properties of the associated function spaces, which depend o…
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…
A variational theory for integral functionals involving finite-horizon fractional gradients
Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
The center of interest in this work are variational problems with integral functionals depending on special nonlocal gradients. The latter correspond to truncated versions of the R…
Extending linear growth functionals to functions of bounded fractional variation
Hidde Schönberger
In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity p…