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Media type:
Text;
E-Article
Title:
Density of convex intersections and applications
Contributor:
Hintermüller, Michael
[Author];
Rautenberg, Carlos N.
[Author];
Rösel, Simon
[Author]
Published:
Weierstrass Institute for Applied Analysis and Stochastics publication server, 2017
Language:
English
DOI:
https://doi.org/10.1098/rspa.2016.0919
ISSN:
1471-2946 -- 0962-8444 -- P Roy Soc A -- Proc R Soc A -- Proc R Soc London A -- Proc R Soc London Ser A -- Proc Roy Soc London Ser A -- Proceedings of the Royal Society A -- 2207134-9 -- 209241-4 -- https://royalsocietypublishing.org/journal/rspa
Footnote:
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Description:
In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.