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E. Davoli, I. Fonseca, P. Liu:
"Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme";
in: "ASC Report 48/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 32.

In this paper, we introduce the notion of separately global solutions for large-strain rate-independent systems, and we provide an existence result for a model describing bulk damage. Our analysis covers non-convex energies blowing up for extreme compressions, yields solutions excluding interpenetration of matter, and allows to handle nonlinear couplings of the deformation and the internal variable featuring both Eulerian and Lagrangian terms. In particular, motivated by the theory developed in [49] in the small strain setting, and for separately convex energies we provide a solution concept suitable for large strain inelasticity.

http://www.asc.tuwien.ac.at/preprint/2020/asc48x2020.pdf