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Creators/Authors contains: "Arndt, Rafael"

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  1. ; (, 2022 IEEE 61st Conference on Decision and Control (CDC))
    Full Text Available 
  2. ; ; ; (, Advances in Nonlinear Analysis)
    Abstract In this article, we consider nondiffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state space being a Sobolev one or the space of functions of bounded variation. We address existence and uniqueness of the model under low regularity assumptions, and rigorously identify its Fenchel pre-dual problem. The latter in some cases is posed on a nonstandard space of Borel measures with square integrable divergences. We also establish existence and uniqueness of solution to this pre-dual problem under some assumptions. We conclude the article by introducing a mixed finite-element method to solve the primal-dual system. The numerical examples illustrate the theoretical findings. 
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  3. ; (, ArXivorg)
    null (Ed.)
    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 control is determined by source locations and intensity thereof. The control problem is described by an optimization problem in function space and constrained by a variational inequality or a non-smooth equation. We address a regularization approach via a family of nonlinear partial differential equations, and provide a novel result of Newton differentiability of the control-to-state map. Further, we discuss solution algorithms for the state equation as well as for the optimization problem. 
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    Accepted Manuscript Full Text Available