22 citations · 32 across the 17 of their papers we have counts for
22 papers
A function space approach to the shape optimization of the Boussinesq system
Andrea Ceretani, Weiwei Hu, Lin Mu +1
We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a tempera…
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…
Optimal Control of a Quasi-Variational Sweeping Process
Harbir Antil, Rafael Arndt, Boris S. Mordukhovich +2
The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionle…
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…
The Spatially Variant Fractional Laplacian
Andrea N. Ceretani, Carlos N. Rautenberg
We introduce a definition of the fractional Laplacian with spatially variable order and study the solvability of the associated Poisson problem on…
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…
On the differentiability of the minimal and maximal solution maps of elliptic quasi-variational inequalities
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
In this note, we prove that the minimal and maximal solution maps associated to elliptic quasi-variational inequalities of obstacle type are directionally differentiable with respe…
Optimal control and directional differentiability for elliptic quasi-variational inequalities
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal c…
Analysis of a quasi-variational contact problem arising in thermoelasticity
Amal Alphonse, Carlos N. Rautenberg, José Francisco Rodrigues
We formulate and study two mathematical models of a thermoforming process involving a membrane and a mould as implicit obstacle problems. In particular, the membrane-mould coupling…
On a Fractional Version of a Murat Compactness Result and Applications
Harbir Antil, Carlos N. Rautenberg, Armin Schikorra
The paper provides an extension, to fractional order Sobolev spaces, of the classical result of Murat and Brezis which states that the positive cone of elements in comp…
Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization
Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg +1
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This…
Variable step mollifiers and applications
Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg
We consider a mollifying operator with variable step that, in contrast to the standard mollification, is able to preserve the boundary values of functions. We prove boundedness of…
On existence and uniqueness of solutions to a Boussinesq system with nonlinear and mixed boundary conditions
Rafael Arndt, Andrea N. Ceretani, Carlos N. Rautenberg
We study a Boussinesq system in a bounded domain with an outlet boundary portion where fluid can leave or re-enter. On this boundary part, we consider a do-nothing condition for th…
Existence, iteration procedures and directional differentiability for parabolic QVIs
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs b…
Stability of the solution set of quasi-variational inequalities and optimal control
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal contro…
Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications
Harbir Antil, Carlos N. Rautenberg
We propose a new variational model in weighted Sobolev spaces with non-standard weights and applications to image processing. We show that these weights are, in general, not of Muc…
Directional differentiability for elliptic quasi-variational inequalities of obstacle type
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The class…
Fractional Elliptic Quasi-Variational Inequalities: Theory and Numerics
Harbir Antil, Carlos N. Rautenberg
This paper introduces an elliptic quasi-variational inequality (QVI) problem class with fractional diffusion of order , studies existence and uniqueness of solutions a…
Analytical aspects of spatially adapted total variation regularisation
Michael Hintermüller, Konstantinos Papafitsoros, Carlos N. Rautenberg
In this paper we study the structure of solutions of the one dimensional weighted total variation regularisation problem, motivated by its application in signal recovery tasks. We…