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Minimal and maximal solution maps of elliptic QVIs of obstacle type: Lipschitz stability, differentiability and optimal control
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg +1
Quasi-variational inequalities (QVIs) of obstacle type in many cases have multiple solutions that can be ordered. We study a multitude of properties of the operator mapping the sou…
Convergence aspects for sets of measures with divergences and boundary conditions
Nicholas Chisholm, Carlos N. Rautenberg
In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider…
On Some Quasi-Variational Inequalities and Other Problems with Moving Sets
José-Luis Menaldi, Carlos N. Rautenberg
Since its introduction over 50 years ago, the concept of Mosco convergence has permeated through diverse areas of mathematics and applied sciences. These include applied analysis,…
Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints
Harbir Antil, Rafael Arndt, Carlos N. Rautenberg +1
In this paper, we consider non-diffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint i…
Differentiability and Control of a Model for Granular Material Accumulation
Rafael Arndt, Carlos N. Rautenberg
We consider differentiability issues associated to the problem of minimizing the accumulation of a granular cohesionless material on a certain surface. The design variable or contr…
Existence, uniqueness, and stabilization results for parabolic variational inequalities
Axel Kröner, Carlos N. Rautenberg, Sérgio S. Rodrigues
In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show…